Stochastic Parabolic Equations of Full Second Order
S. V. Lototsky, B. L. Rozovskii
TL;DR
This paper introduces a method for solving second-order parabolic stochastic PDEs using Wiener Chaos expansion, establishing existence and uniqueness of solutions in this context.
Contribution
It develops a generalized solution framework for second-order parabolic stochastic PDEs employing Cameron-Martin Wiener Chaos expansion, a novel approach in this area.
Findings
Established existence and uniqueness of Wiener Chaos solutions for these PDEs.
Provided a procedure for defining generalized solutions using Wiener Chaos expansion.
Extended the theory of stochastic PDEs to include full second-order operators.
Abstract
A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for parabolic stochastic PDEs such that both the drift and the diffusion operators are of the second order.
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Taxonomy
TopicsDifferential Equations and Numerical Methods