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Recurso libre

Ito Formula and Local Time for the Fractional Brownian Sheet
Tudor, Ciprian A.; Laboratoire de Probabilit'{e}s, Universit'{e} de Paris 6 - Viens, Frederi G.; Purdue University

Formato:	Peer-reviewed Article,
Enlaces:	Using the techniques of the stochastic calculus of variations for Gaussian processes, we derive an It^{o} formula for the fractional Brownian sheet with Hurst parameters bigger than $1/2$. As an application, we give a stochastic integral representation for the local…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

Computation of Moments for the Length of the OneDimensional ISE Support
Delmas, Jean-Francois; École des Ponts

Formato:	Peer-reviewed Article,
Enlaces:	We consider in this paper the support $[L',R']$ of the one dimensional Integrated Super Brownian Excursion. We determine the distribution of $(R',L')$ through a modified Laplace transform. Then we give an explicit value for the first two moments of $R'$…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

Excited Random Walk on Trees
Volkov, Stanislav; University of Bristol, UK

Formato:	Peer-reviewed Article,
Enlaces:	We consider a nearest-neighbor stochastic process on a rooted tree $G$ which goes toward the root with probability $1-\varepsilon$ when it visits a vertex for the first time. At all other times it behaves like a simple random walk on…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

Some Non-Linear S.P.D.E's That Are Second Order In Time
Dalang, Robert C.; Ecole Polytechnique Fédérale - Mueller, Carl; University of Rochester

Formato:	Peer-reviewed Article,
Enlaces:	We extend J.B. Walsh's theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation, and driven by spatially homogeneous Gaussian noise. For…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

Reflected Backward Stochastic Differential Equation with Jumps and Random Obstacle
Hamadène, Said; Universite du Maine - Ouknine, Youssef; Universite Cadi Ayyad

Formato:	Peer-reviewed Article,
Enlaces:	In this paper we give a solution for the one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process. We prove existence and uniqueness of the solution in using…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

Fractional Ornstein-Uhlenbeck processes
Cheridito, Patrick; ETH Zurich - Kawaguchi, Hideyuki; Keio University and Sumitomo Mitsui Banking Corporation - Maejima, Makoto; Keio University

Formato:	Peer-reviewed Article,
Enlaces:	The classical stationary Ornstein-Uhlenbeck process can be obtained in two different ways. On the one hand, it is a stationary solution of the Langevin equation with Brownian motion noise. On the other hand, it can be obtained from Brownian motion…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

On Convergence of Population Processes in Random Environments to the Stochastic Heat Equation with Colored Noise
Sturm, Anja; Technische Universität Berlin

Formato:	Peer-reviewed Article,
Enlaces:	We consider the stochastic heat equation with a multiplicative colored noise term on the real space for dimensions greater or equal to 1. First, we prove convergence of a branching particle system in a random environment to this stochastic heat…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

The Norm of the Product of a Large Matrix and a Random Vector
Böttcher, Albrecht; TU Chemnitz - Grudsky, Sergei; CINVESTAV del I.P.N.

Formato:	Peer-reviewed Article,
Enlaces:	Given a real or complex $n \times n$ matrix $A_n$, we compute the expected value and the variance of the random variable $\\| A_n x\\|^2/\\| A_n \\|^2$, where $x$ is uniformly distributed on the unit sphere of $R^n$ or $C^n$.…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

Competing Species Superprocesses with Infinite Variance
Fleischmann, Klaus; Weierstrass Institute for Applied Analysis and Stochastics - Mytnik, Leonid; Technion - Israel Institute of Technology

Formato:	Peer-reviewed Article,
Enlaces:	We study pairs of interacting measure-valued branching processes (superprocesses) with alpha-stable migration and $(1+\beta)$-branching mechanism. The interaction is realized via some killing procedure. The collision local time for such processes is constructed as a limit of approximating collision local times.…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

10.

Berry-Esseen Bounds for the Number of Maxima in Planar Regions
Bai, Zhi-Dong; National University of Singapore and Northeast Normal University - Hwang, Hsien-Kuei; Academia Sinica, Taipei - Tsai, Tsung-Hsi; Academia Sinica, Taipei

Formato:	Peer-reviewed Article,
Enlaces:	We derive the optimal convergence rate $O(n^{-1/4})$ in the central limit theorem for the number of maxima in random samples chosen uniformly at random from the right equilateral triangle with two sides parallel to the axes, the hypotenuse with the…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

11.

Brownian Motion on Compact Manifolds: Cover Time and Late Points
Dembo, Amir; Stanford University - Peres, Yuval; University of California, Berkeley - Rosen, Jay; College of Staten Island, CUNY

Formato:	Peer-reviewed Article,
Enlaces:	Let $M$ be a smooth, compact, connected Riemannian manifold of dimension $d>2$ and without boundary. Denote by $T(x,r)$ the hitting time of the ball of radius $r$ centered at $x$ by Brownian motion on $M$. Then, $C_r(M)=\sup_{x \in M} T(x,r)$…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

12.

Clustering Behavior of a Continuous-Sites Stepping-Stone Model with Brownian Migration
Zhou, Xiaowen; Department of Mathematics and Statistics, Concordia university

Formato:	Peer-reviewed Article,
Enlaces:	Clustering behavior is studied for a continuous-sites stepping-stone model with Brownian migration. It is shown that, if the model starts with the same mixture of different types of individuals over each site, then it will evolve in a way such…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

13.

Homogeneous Random Measures and Strongly Supermedian Kernels of a Markov Process
Fitzsimmons, Patrick J.; UCSD - Getoor, Ronald K.; UCSD

Formato:	Peer-reviewed Article,
Enlaces:	The potential kernel of a positive left additive functional (of a strong Markov process $X$) maps positive functions to strongly supermedian functions and satisfies a variant of the classical domination principle of potential theory. Such a kernel $V$ is called…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

14.

Large Deviation Principle for a Stochastic Heat Equation With Spatially Correlated Noise
Marquez-Carreras, David; Universitat de Barcelona - Sarra, Monica; Universitat de Barcelona

Formato:	Peer-reviewed Article,
Enlaces:	In this paper we prove a large deviation principle (LDP) for a perturbed stochastic heat equation defined on $[0,T]\times [0,1]^d$. This equation is driven by a Gaussian noise, white in time and correlated in space. Firstly, we show the Holder…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

15.

Comparison Theorems for Small Deviations of Random Series
Gao, Fuchang; University of Idaho - Hannig, Jan; Colorado State University - Torcaso, Fred; Johns Hopkins University

Formato:	Peer-reviewed Article,
Enlaces:	Let ${\xi_n}$ be a sequence of i.i.d. positive random variables with common distribution function $F(x)$. Let ${a_n}$ and ${b_n}$ be two positive non-increasing summable sequences such that ${\prod_{n=1}^{\infty}(a_n/b_n)}$ converges. Under some mild assumptions on $F$, we prove the following comparison…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

16.

Laplace Transforms via Hadamard Factorization
Gao, Fuchang; University of Idaho - Hannig, Jan; Colorado State University - Lee, Tzong-Yow; University of Maryland - Torcaso, Fred; The Johns Hopkins University

Formato:	Peer-reviewed Article,
Enlaces:	In this paper we consider the Laplace transforms of some random series, in particular, the random series derived as the squared $L_2$ norm of a Gaussian stochastic process. Except for some special cases, closed form expressions for Laplace transforms are,…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

17.

Large Deviations for the Emprirical Measures of Reflecting Brownian Motion and Related Constrained Processes in $R_+$
Budhiraja, Amarjit; University of North Carolina at Chapel Hill - Dupuis, Paul; Brown University

Formato:	Peer-reviewed Article,
Enlaces:	We consider the large deviations properties of the empirical measure for one dimensional constrained processes, such as reflecting Brownian motion, the M/M/1 queue, and discrete time analogues. Because these processes do not satisfy the strong stability assumptions that are usually…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

18.

Long-Memory Stable Ornstein-Uhlenbeck Processes
Maejima, Makoto; Department of Mathematics, Keio University - Yamamoto, Kenji; Department of Mathematics, Keio University

Formato:	Peer-reviewed Article,
Enlaces:	The solution of the Langevin equation driven by a Lévy process noise has been well studied, under the name of Ornstein-Uhlenbeck type process. It is a stationary Markov process. When the noise is fractional Brownian motion, the covariance of the…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

19.

Exponential Asymptotic Stability of Linear Ito-Volterra Equation with Damped Stochastic Perturbations
Appleby, John A. D.; Dublin City University, Ireland - Freeman, Alan; Dublin City University, Ireland

Formato:	Peer-reviewed Article,
Enlaces:	This paper studies the convergence rate of solutions of the linear Ito-Volterra equation $$ dX(t) = \left(AX(t) + \int_{0}^{t} K(t-s)X(s),ds\right)\,dt + \Sigma(t)\,dW(t) \tag{1} $$ where $K$ and $\Sigma$ are continuous matrix-valued functions defined on $\mathbb{R}^{+}$, and $(W(t))_{t \geq 0}$ is…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

20.

Degenerate Variance Control in the One-dimensional Stationary Case
Ocone, Daniel L; Rutgers University - Weerasinghe, Ananda; Iowa State University

Formato:	Peer-reviewed Article,
Enlaces:	We study the problem of stationary control by adaptive choice of the diffusion coefficient in the case that control degeneracy is allowed and the drift admits a unique, asymptotically stable equilibrium point. We characterize the optimal value and obtain it…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

21.

Branching Random Walk with Catalysts
Kesten, Harry; Cornell University - Sidoravicius, Vladas; IMPA

Formato:	Peer-reviewed Article,
Enlaces:	Shnerb et al. (2000), (2001) studied the following system of interacting particles on $\Bbb Z^d$: There are two kinds of particles, called $A$-particles and $B$-particles. The $A$-particles perform continuous time simple random walks, independently of each other. The jumprate of…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

22.

Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales
Gradinaru, Mihai; Institut de Math'ematiques 'Elie Cartan, Universit'e Henri Poincar'e - Nourdin, Ivan; Institut de Math'ematiques 'Elie Cartan, Universit'e Henri Poincar'e

Formato:	Peer-reviewed Article,
Enlaces:	Let $X$ be the fractional Brownian motion of any Hurst index $H\in (0,1)$ (resp. a semimartingale) and set $\alpha=H$ (resp. $\alpha=\frac{1}{2}$). If $Y$ is a continuous process and if $m$ is a positive integer, we study the existence of the…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

23.

Distributions of Sojourn Time, Maximum and Minimum for Pseudo-Processes Governed by Higher-Order Heat-Type Equations
Lachal, Aime; Institut National des Sciences Appliquées de Lyon, France

Formato:	Peer-reviewed Article,
Enlaces:	The higher-order heat-type equation $ \partial u/\partial t=\pm\partial^{n} u/ \partial x^{n} $ has been investigated by many authors. With this equation is associated a pseudo-process $(X_t)_{t\ge 0}$ which is governed by a signed measure. In the even-order case, Krylov (1960)…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability

Recurso libre

24.

State Dependent Multitype Spatial Branching Processes and their Longtime Behavior
Dawson, Donald A.; Carleton University - Greven, Andreas; Universitat Erlangen-Nurnberg

Formato:	Peer-reviewed Article,
Enlaces:	The paper focuses on spatial multitype branching systems with spatial components (colonies) indexed by a countable group, for example $Z^d$ or the hierarchical group. As type space we allow continua and describe populations in one colony as measures on the…
Fecha:	2003-01-01
Recurso:	Electronic journal of probability