A semilinear parabolic equation on R d with a non-additive random perturbation is studied.
The noise is supposed to be a spatially homogeneous Wiener process. Conditions for the …

We develop a novel theory of weak and strong stochastic integration for cylindrical
martingale-valued measures taking values in the dual of a nuclear space. This is applied to …

A stochastic integral with respect to a generalized, ie, not necessarily time-homogeneous,
Wiener process in the dual of a nuclear space is defined. The integrands are random linear …

The aim of this work is to present, in self-contained form, results concerning fundamental
and the most important questions related to linear stochastic Volterra equations of …

We study regularity of stochastic convolutions solving Volterra equations on R d driven by a
spatially homogeneous Wiener process. General results are applied to stochastic parabolic …

Generalized (distribution-valued) Ornstein-Uhlenbeck processes, which by definition are
solutions of generalized Langevin equations, arise in many investigations on fluctuation …

In this paper we develop a criterion for existence or non-existence of self-intersection local
time (SILT) for a wide class of Gaussian L′(R d)-valued processes, we show that quite …

Full article: Stochastic Heat and Wave Equations on a Lie Group Skip to Main Content Taylor
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A system of particles of k types with immigration in R d is considered. Each particle,
according to its type, independently migrates following a symmetric stable process, lives an …

Existence and continuity results are obtained for self-intersection local time of-valued
Ornstein–Uhlenbeck processes, where X0 is Gaussian, Wt is an-Wiener process …