Related papers: On a Class of Martingale Problems on Banach Spaces
A class of stochastic delay equations in Banach space $E$ driven by cylindrical Wiener process is studied. We investigate two concepts of solutions: weak and generalised strong, and give conditions under which they are equivalent. We…
We study a class of stochastic evolution equations in a Banach space $E$ driven by cylindrical Wiener process. Three different concept of solutions: generalised strong, weak and mild are defined and the conditions under which they are…
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L_p$ spaces, driven by multiplicative Wiener noise, with a drift term given by an evaluation operator that is assumed to be…
We study the Cauchy problem for a semilinear stochastic partial differential equation driven by a finite-dimensional Wiener process. In particular, under the hypothesis that all the coefficients are sufficiently smooth and have bounded…
We prove existence of weak solutions (in the probabilistic sense) for a general class of stochastic semilinear wave equations on bounded domains of $R^d$ driven by a possibly discontinuous square integrable martingale.
We introduce and discuss L\'evy-type cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a one-to-one relation to weak solutions of stochastic…
We study the convergence of semilinear parabolic stochastic evolution equations, posed on a sequence of Banach spaces approximating a limiting space and driven by additive white noise projected onto the former spaces. Under appropriate…
We prove existence and uniqueness of mild and generalized solutions for a class of stochastic semilinear evolution equations driven by additive Wiener and Poisson noise. The non-linear drift term is supposed to be the evaluation operator…
We prove existence and uniqueness of strong solutions for a class of semilinear stochastic evolution equations driven by general Hilbert space-valued semimartingales, with drift equal to the sum of a linear maximal monotone operator in…
We obtain estimates on the first-order Malliavin derivative of mild solutions, evaluated at fixed points in time and space, to a class of parabolic dissipative stochastic PDEs on bounded domain of $\mathbb{R}^d$. In particular, such…
This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear…
By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equation of rate-independent type. Approximate solutions are…
We construct planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-Shepp-type equations and a change-of-variable formula in the spirit of Freidlin-Sheu for these so-called "Walsh…
The existence of global martingale weak solution for the 2D and 3D stochastic Cahn-Hilliard-Navier-Stokes equations driven by multiplicative noise in a smooth bounded domain is established. In particular, the system is supplied with the…
Comparison results for Markov processes w.r.t. function class induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…
We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise.We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong…
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L^p$ spaces on bounded domains of $\mathbb{R}^n$ with a nonlinear drift term given by the superposition operator generated by a…
We prove a modification to the classical maximal inequality for stochastic convolutions in 2-smooth Banach spaces using the factorization method. This permits to study semilinear stochastic partial differential equations with unbounded…
It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale…