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…

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.

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…

A non-commutative version of the sewing lemma is proved, with some applications

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.

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…

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…

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.

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.

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…