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We prove a Chung's law of the iterated logarithm for recurrent linear Markov processes. In order to attain this level of generality, our normalization is random. In particular, when the Markov process in question is a diffusion, we obtain the…

The question considered in this paper is which sequences of $p$-integrable random variables can be represented as conditional expectations of a fixed random variable with respect to a given sequence of sigma-fields. For finite families of sigma-fields, explicit inequality equivalent…

We study the metastability of the stochastic three dimensional Ising model on a finite torus under a small positive magnetic field at very low temperatures.

Following Lyons (1990, Random Walks and Percolation on Trees) we define a periodic tree, restate its branching number and consider a biased random walk on it. In the case of a transient walk, we describe the walk-invariant random periodic tree…

In this paper we show that the set of points where the density of a Wiener functional is strictly positive is an open connected set, assuming some regularity conditions.

We present new methods for proving the convergence of the classical approximations of the Stratonovitch equation. We especially make use of the fractional Liouville-valued Sobolev space $W^{r,p}({\cal J}_{\alpha,p})$. We then obtain a support theorem for the capacity $c_{r,p}$.

We show existence of measure attractors for 2-D stochastic Navier-Stokes equations with general multiplicative noise.

The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in $cH^2_p(T)$-space are proved.

We obtain a Laplace asymptotic expansion, in orders of $\lambda$, of $$ E^\rho_x \left\{ G(\lambda x) e^{-\lambda ^{-2} F(\lambda x)}\right\}$$ the expectation being with respect to a Gaussian process. We extend a result of Pincus and build upon the previous…