arXiv subjects
Publications and source records attributed to Anna Karczewska.
This paper is devoted to a construction of the stochastic Itô integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the introduced integral with the integral defined by Walsh [9] is provided as well.
In the paper we study some numerical solutions to Volterra equations which interpolate heat and wave equations. We present a scheme for construction of approximate numerical solutions for one and two spatial dimensions. Some solutions to the stochastic version of such equations (for one spatial dimension) are presented as well.
We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued convolutions in terms of the covariance kernel of a noise given by spatially homogeneous Wiener process.
In the paper we study stochastic convolution appearing in Volterra equation driven by so called Lévy process. By Lévy process we mean a process with homogeneous independent increments, continuous in probability and cadlag.
The aim of the paper is to demonstrate the use of the Galerkin method for some kind of Volterra equations, determininistic and stochastic as well. The paper consists of two parts: the theoretical and numerical one. In the first part we recall some apparently well-known results concerning the Volterra equations under consideration. In the second one we describe a numerical algorithm used and next present some examples of numerical solutions in order to illustrate the pertinent features of the technique used in the paper.