Nonlinear stochastic functional integral equations in the plane.

Turo, Jan

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Different types of uniqueness (e.g. pathwise uniqueness, uniqueness in law, joint uniqueness in law) and existence (e.g. strong solution, martingale solution) for stochastic evolution equations driven by a Wiener process are studied and compared. We show a sufficient condition for a joint distribution of a process and a Wiener process to be a solution of a given SPDE. Equivalences between different concepts of solution are shown. An alternative approach to the construction of the stochastic...

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The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of solutions (in Itô's sense) for a rather general type of stochastic PDE's with non-linear monotone operators and with delays.