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…

For a function $\ell$ satisfying suitable integrability (but not continuity) requirements, we construct a process $(B^\ell_u, 0 \leq u \leq 1)$ interpretable as Brownian excursion conditioned to have local time $\ell(\cdot)$ at time $1$. The construction is achieved by first…

Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to: An efficient algorithm to approximate the process. An ergodic theorem which…

We provide necessary and sufficient conditions for hypercontractivity of the minima of nonnegative, i.i.d. random variables and of both the maxima of minima and the minima of maxima for such r.v.'s. It turns out that the idea of hypercontractivity for…

The multiplicative coalescent $X(t)$ is a $l^2$-valued Markov process representing coalescence of clusters of mass, where each pair of clusters merges at rate proportional to product of masses. From random graph asymptotics it is known (Aldous (1997)) that there exists…

Branching measure-valued diffusion models are investigated that can be regarded as pairs of historical Brownian motions modified by a competitive interaction mechanism under which individuals from each population have their longevity or fertility adversely affected by collisions with individuals from…