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A stochastic scheme of approximation for ordinary differential equations
Fierro, Raul; Universidad Catolica de Valparaiso - Torres, Soledad; Universidad de Valparaiso

Formato:	Peer-reviewed Article,
Enlaces:	In this note we provide a stochastic method for approximating solutions of ordinary differential equations. To this end, a stochastic variant of the Euler scheme is given by means of Markov chains. For an ordinary differential equation, these approximations are…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

Large deviation principles for Markov processes via Phi-Sobolev inequalities
Wu, Liming; Wuhan University and Université Blaise Pascal - Yao, Nian; Wuhan University

Formato:	Peer-reviewed Article,
Enlaces:	Via Phi-Sobolev inequalities, we give some sharp integrability conditions on $F$ for the large deviation principle of the empirical mean $\frac{1}{T}{\int_{0}^{T}{F(X_{s})}ds}$ for large time $T$, where $F$ is unbounded with values in some separable Banach space. Several examples are provided.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

Threshold phenomena on product spaces: BKKKL revisited (once more)
Rossignol, Raphaël; Université Paris 11, France

Formato:	Peer-reviewed Article,
Enlaces:	We revisit the work of Bourgain et al. (1992) - referred to as "BKKKL" in the title - about influences on Boolean functions in order to give a precise statement of threshold phenomenon on the product space $\{1,...,r\}^N$, generalizing one…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

A non-commutative sewing lemma
Feyel, Denis; Université Evry - de La Pradelle, Arnaud; Universite Paris VI - Mokobodzki, Gabriel; Universite Paris VI

Formato:	Peer-reviewed Article,
Enlaces:	A non-commutative version of the sewing lemma is proved, with some applications
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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A remark on the equivalence of Gaussian processes
van Zanten, Harry; Vrije Universiteit Amsterdam

Formato:	Peer-reviewed Article,
Enlaces:	In this note we extend a classical equivalence result for Gaussian stationary processes to the more general setting of Gaussian processes with stationary increments. This will allow us to apply it in the setting of aggregated independent fractional Brownian motions.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space
Le Prince, Vincent; IRMAR, Rennes

Formato:	Peer-reviewed Article,
Enlaces:	We establish in this paper an exact formula which links the dimension of the harmonic measure, the asymptotic entropy and the rate of escape for a random walk on a discrete subgroup of the isometry group of a Gromov hyperbolic…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

Corners and Records of the Poisson Process in Quadrant
Gnedin, Alexander; Utrecht University

Formato:	Peer-reviewed Article,
Enlaces:	The scale-invariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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Optimising prediction error among completely monotone covariance sequences
McVinish, Ross S; Queensland University of Technology

Formato:	Peer-reviewed Article,
Enlaces:	We provide a characterisation of Gaussian time series which optimise the one-step prediction error subject to the covariance sequence being completely monotone with the first m covariances specified.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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Entropy Estimate for $k$-Monotone Functions via Small Ball Probability of Integrated Brownian Motions
Gao, Fuchang; University of Idaho

Formato:	Peer-reviewed Article,
Enlaces:	Metric entropy of the class of probability distribution functions on $[0,1]$ with a $k$-monotone density is studied through its connection with the small ball probability of $k$-times integrated Brownian motions.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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10.

On the boundedness of Bernoulli processes over thin sets
Latala, Rafal; University of Warsaw

Formato:	Peer-reviewed Article,
Enlaces:	We show that the Bernoulli conjecture holds for sets with small one-dimensional projections, i.e. any bounded Bernoulli process indexed by such set may be represented as a sum of a uniformly bounded process and a process dominated by a bounded…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

11.

Filtering and parameter estimation for a jump stochastic process with discrete observations
Makhnin, Oleg V; New Mexico Tech

Formato:	Peer-reviewed Article,
Enlaces:	A compound Poisson process is considered. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem) in Bayesian setting. We obtain bounds for the asymptotic rate of the expected square error of…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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12.

Symmetrization of Bernoulli
Pal, Soumik; Cornell University

Formato:	Peer-reviewed Article,
Enlaces:	We show that an asymmetric Bernoulli random variable is symmetry resistant in the sense that any independent random variable, which when added to it produces a symmetric sum, must have a variance at least as much as itself. The main…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

13.

On differentiability of the Parisi formula
Panchenko, Dmitry; Texas A&M University

Formato:	Peer-reviewed Article,
Enlaces:	It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

14.

On the sphericity of scaling limits of random planar quadrangulations
Miermont, Grégory; Fondation des Sciences Mathématiques de Paris

Formato:	Peer-reviewed Article,
Enlaces:	We give a new proof of a theorem by Le Gall and Paulin, showing that scaling limits of random planar quadrangulations are homeomorphic to the 2-sphere. The main geometric tool is a reinforcement of the notion of Gromov-Hausdorff convergence, called…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

15.

Internal Diffusion-Limited Aggregation on non-amenable graphs
Huss, Wilfried; Graz University of Technology

Formato:	Peer-reviewed Article,
Enlaces:	The stochastic growth model Internal Diffusion Limited Aggregation was defined in 1991 by Diaconis and Fulton. Several shape results are known when the underlying state space is the d-dimensional lattice, or a discrete group with exponential growth. We prove an…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

16.

A note on the distributions of the maximum of linear Bernoulli processes
Bobkov, Sergey G; University of Minnesota

Formato:	Peer-reviewed Article,
Enlaces:	We give a characterization of the family of all probability measures on the extended line $(-\infty,+\infty]$, which may be obtained as the distribution of the maximum of some linear Bernoulli process.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

17.

Exact Convergence Rate for the Maximum of Standardized Gaussian Increments
Kabluchko, Zakhar; Goettingen University - Munk, Axel; Goettingen University

Formato:	Peer-reviewed Article,
Enlaces:	We prove an almost sure limit theorem on the exact convergence rate of the maximum of standardized gaussian random walk increments. This gives a more precise version of Shao's theorem ( Shao, Q.-M., 1995. On a conjecture of R&eacutev&eacutesz. Proc.…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

18.

Continuous-time trading and the emergence of volatility
Vovk, Vladimir; Royal Holloway, University of London

Formato:	Peer-reviewed Article,
Enlaces:	This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of non-constant price processes has to be 2, as in the…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

19.

A functional limit theorem for a 2d-random walk with dependent marginals
Guillotin-Plantard, Nadine; Université Lyon 1 - Le Ny, Arnaud; Université Paris Sud

Formato:	Peer-reviewed Article,
Enlaces:	We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

20.

On the relationship between subordinate killed and killed subordinate processes
Song, Renming; University of Illinois at Urbana-Champaign - Vondracek, Zoran; University of Zagreb

Formato:	Peer-reviewed Article,
Enlaces:	We study the precise relationship between the subordinate killed and killed subordinate processes in the case of an underlying Hunt process, and show that, under minimal conditions, the former is a subprocess of the latter obtained by killing at a…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

21.

Infinite Divisibility of Gaussian Squares with Non-zero Means
Marcus, Michael B.; The City College of CUNY - Rosen, Jay; The College of Staten Island of CUNY

Formato:	Peer-reviewed Article,
Enlaces:	We give necessary and sufficient conditions for a Gaussian vector with non-zero mean, to have infinitely divisible squares for all scalar multiples of the mean, and show how the this vector is related to the local times of a Markov…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

22.

Sharp estimates for the convergence of the density of the Euler scheme in small time
Gobet, Emmanuel; Laboratoire Jean Kuntzmann Université de Grenoble - Labart, Céline; INRIA Paris Rocquencourt

Formato:	Peer-reviewed Article,
Enlaces:	In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

23.

On Asymptotic Growth of the Support of Free Multiplicative Convolutions
Kargin, Vladislav; Courant Institute of Mathematical Sciences

Formato:	Peer-reviewed Article,
Enlaces:	Let $\mu$ be a compactly supported probability measure on $\mathbb{R}^{+}$ with expectation $1$ and variance $V.$ Let $\mu _{n}$ denote the $n$-time free multiplicative convolution of measure $\mu $ with itself. Then, for large $n$ the length of the support…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

24.

Perfect sampling from the limit of deterministic products of stochastic matrices
Stenflo, Örjan; Uppsala University

Formato:	Peer-reviewed Article,
Enlaces:	We illustrate how a technique from the theory of random iterations of functions can be used within the theory of products of matrices. Using this technique we give a simple proof of a basic theorem about the asymptotic behavior of…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

25.

Distribution of a random functional of a Ferguson-Dirichlet process over the unit sphere
Jiang, Thomas Jyh-Ming; National Chengchi University - Kuo, Kun-Lin; Academia Sinica

Formato:	Peer-reviewed Article,
Enlaces:	Jiang, Dickey, and Kuo [12] gave the multivariate c-characteristic function and showed that it has properties similar to those of the multivariate Fourier transformation. We first give the multivariate c-characteristic function of a random functional of a Ferguson-Dirichlet process over…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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26.

A martingale on the zero-set of a holomorphic function
Kink, Peter; Faculty for Computer and Information Sciences, University of Ljubljana

Formato:	Peer-reviewed Article,
Enlaces:	We give a simple probabilistic proof of the classical fact from complex analysis that the zeros of a holomorphic function of several variables are never isolated and that they are not contained in any compact set. No facts from complex…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

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27.

Distribution of the Brownian motion on its way to hitting zero
Chigansky, Pavel; The Hebrew University - Klebaner, Fima C.; Monash University

Formato:	Peer-reviewed Article,
Enlaces:	For the one-dimensional Brownian motion $B=(B_t)_{t\geq 0}$, started at $x>0$, and the first hitting time $\tau=\inf\{t\geq 0:B_t=0\}$, we find the probability density of $B_{u\tau}$ for a $u\in(0,1)$, i.e. of the Brownian motion on its way to hitting zero.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

28.

Sharp inequality for bounded submartingales and their differential subordinates
Osekowski, Adam; University of Warsaw

Formato:	Peer-reviewed Article,
Enlaces:	Let $\alpha$ be a fixed number from the interval $[0,1]$. We obtain the sharp probability bounds for the maximal function of the process which is $\alpha$-differentially subordinate to a bounded submartingale. This generalizes the previous results of Burkholder and Hammack.
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

29.

Renewal series and square-root boundaries for Bessel processes
Enriquez, Nathanael; Universite Paris 10 - Sabot, Christophe; Université de Lyon 1 - Yor, Marc; Universite Paris 6

Formato:	Peer-reviewed Article,
Enlaces:	We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical results by Breiman and Shepp, concerning Brownian…
Fecha:	2008-01-01
Recurso:	Electronic communications in probability

Recurso libre

30.

Reflected Brownian motion in a wedge: sum-of-exponential stationary densities
Dieker, A.B.; Georgia Institute of Technology - Moriarty, J.; University of Manchester

Formato:	Peer-reviewed Article,
Enlaces:	We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relying on geometric ideas reminiscent of the reflection principle,…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

31.

Uniqueness of the mixing measure for a random walk in a random environment on the positive integers
Eckhoff, Maren; Technical University of Munich - Rolles, Silke W.W.; Technical University of Munich

Formato:	Peer-reviewed Article,
Enlaces:	Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An application to linearly edge-reinforced random walk is given.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

32.

Note: Random-to-front shuffles on trees
Bjorner, Anders; Royal Institute of Technology

Formato:	Peer-reviewed Article,
Enlaces:	A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local ``random-to-front'' reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the transition matrix are determined using…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

33.

Orthogonality and probability: beyond nearest neighbor transitions
Kovchegov, Yevgeniy V; Oregon State University

Formato:	Peer-reviewed Article,
Enlaces:	In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest neighbor processes, but failed beyond nearest neighbor transitions. We will proceed by suggesting and…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

34.

The scaling limit of senile reinforced random walk.
Holmes, Mark P; University of Auckland

Formato:	Peer-reviewed Article,
Enlaces:	This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable conditions, when T has heavy tails the…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

35.

A local limit theorem for the critical random graph
van der Hofstad, Remco W; Technische Universiteit Eindhoven - Kager, Wouter; VU University - Müller, Tobias; Tel Aviv University

Formato:	Peer-reviewed Article,
Enlaces:	We consider the limit distribution of the orders of the $k$ largest components in the Erdos-Rényi random graph inside the "critical window" for arbitrary $k$. We prove a local limit theorem for this joint distribution and derive an exact expression…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

36.

Small time expansions for transition probabilities of some Lévy processes
Marchal, Philippe; CNRS and DMA, Ecole Normale Supérieure

Formato:	Peer-reviewed Article,
Enlaces:	We show that there exist Lévy processes $(X_t,t \geq 0)$ and reals $y>0$ such that for small $t$, the probability $P(X_t> y)$ has an expansion involving fractional powers or more general functions of $t$. This constrasts with previous results giving…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

37.

Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon
Janssen, A.J.E.M; Philips Research - Van Leeuwaarden, J.S.H.; Eindhoven University of Technology and EURANDOM

Formato:	Peer-reviewed Article,
Enlaces:	A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian mo- tion and its sampled version, an expansion is derived with coefficients in terms…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

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38.

Characterization of distributions with the length-bias scaling property
Lopez-Garcia, Marcos; Instituto de Matematicas, UNAM

Formato:	Peer-reviewed Article,
Enlaces:	This paper characterizes the density functions of absolutely continuous positive random variables with finite expectation whose respective distribution functions satisfy the so-called length-bias scaling property.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

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39.

An Almost Sure Limit Theorem For the Maxima of Strongly Dependent Gaussian Sequences
Lin, Fuming; Sichuan University of Science and Engineering

Formato:	Peer-reviewed Article,
Enlaces:	In this paper, we prove an almost sure limit theorem for the maxima of strongly dependent Gaussian sequences under some mild conditions. The result is an expansion of the weakly dependent result of E. Csaki and K. Gonchigdanzan.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

40.

Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift
Gao, Fuqing; Wuhan University - Jiang, Hui; Nanjing University of Aeronautics

Formato:	Peer-reviewed Article,
Enlaces:	Some deviation inequalities and moderate deviation principles for the maximum likelihood estimators of parameters in an Ornstein-Uhlenbeck process with linear drift are established by the logarithmic Sobolev inequality and the exponential martingale method.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

41.

Non-perturbative approach to random walk in markovian environment
Dolgopyat, Dmitry; University of Maryland - Liverani, Carlangelo; Universito of Rome 2

Formato:	Peer-reviewed Article,
Enlaces:	We prove the CLT for a random walk in a dynamical environment where the states of the environment at different sites are independent Markov chains.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

42.

An optimal Itô formula for Lévy processes
Eisenbaum, Nathalie; LPMA, Université Paris 6 - Walsh, Alexander; LPMA, Université Paris 6

Formato:	Peer-reviewed Article,
Enlaces:	Several Itô formulas have been already established for Lévy processes. We explain according to which criteria they are not optimal and establish an extended Itô formula that satisfies that criteria. The interest, in particular, of this formula is to obtain…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

43.

Tesselation of a triangle by repeated barycentric subdivision
Hough, Robert D; Stanford University

Formato:	Peer-reviewed Article,
Enlaces:	Under iterated barycentric subdivision of a triangle, most triangles become flat in the sense that the largest angle tends to $\pi$. By analyzing a random walk on $SL_2(\mathbb{R})$ we give asymptotics with explicit constants for the number of flat triangles…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

44.

Standard representation of multivariate functions on a general probability space
Janson, Svante; Uppsala University

Formato:	Peer-reviewed Article,
Enlaces:	It is well-known that a random variable, i.e. a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

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45.

Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion
Tudor, Ciprian A.; Universte de Paris 1

Formato:	Peer-reviewed Article,
Enlaces:	Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

46.

Concentration of the spectral measure of large Wishart matrices with dependent entries
Guntuboyina, Adityanand; Yale University - Leeb, Hannes; Yale University

Formato:	Peer-reviewed Article,
Enlaces:	We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

47.

On the re-rooting invariance property of Lévy trees
Duquesne, Thomas; Université Pierre et Marie Curie - Le Gall, Jean-Francois; Université Paris-Sud

Formato:	Peer-reviewed Article,
Enlaces:	We prove a strong form of the invariance under re-rooting of the distribution of the continuous random trees called Lévy trees. This expends previous results due to several authors.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

48.

Uniform bounds for exponential moment of maximum of a Dyck path
Khorunzhiy, Oleksiy; Université de Versailles, France - Marckert, Jean-François; CNRS, LabRI, Université de Bordeaux

Formato:	Peer-reviewed Article,
Enlaces:	Let us consider the maximum $M(D)$ of a Dyck path $D$ chosen uniformly in the set of Dyck paths with $2n$ steps. We prove that the exponential moment of $M(D)$ normalized by the square root of $n$ is bounded in…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

Recurso libre

49.

A note on new classes of infinitely divisible distributions on $\mathbb{R}^d$
Maejima, Makoto; Keio University - Nakahara, Genta; Keio University

Formato:	Peer-reviewed Article,
Enlaces:	This paper introduces and studies a family of new classes of infinitely divisible distributions on $\mathbb{R}^d$ with two parameters. Depending on parameters, these classes connect the Goldie-Steutel-Bondesson class and the class of generalized type $G$ distributions, connect the Thorin class…
Fecha:	2009-01-01
Recurso:	Electronic communications in probability

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50.

Density fluctuations for a zero-range process on the percolation cluster
Goncalves, Patricia C.; CMAT - U. Minho - Jara, Milton D.; Paris Dauphine

Formato:	Peer-reviewed Article,
Enlaces:	We prove that the density fluctuations for a zero-range process evolving on the $d$-dimensional supercritical percolation cluster, with $d\geq{3}$, are given by a generalized Ornstein-Uhlenbeck process in the space of distributions $\mathscr{S}'(\mathbb{R}^d)$.
Fecha:	2009-01-01
Recurso:	Electronic communications in probability