This article is cited in 4 papers

Parabolic Itô equations with nonsmooth nonlinearity and duality approach

N. G. Dokuchaev

St. Petersburg State University, Research Institute of Mathematics and Mechanics

Abstract: This paper studies nonlinear stochastic partial differential equations with nonsmooth maximum type nonlinearity. The original equation is studied together with its adjoint equation being a backward stochastic parabolic equation, and together with an auxiliary optimal control problem. Conditions of solvability and uniqueness are obtained. In addition, it is shown that the solution is nonnegative if the free term is nonnegative.

Keywords: parabolic Itô equations, backward equations, stochastic control problems.

Received: 16.08.1999
Revised: 02.10.2000

DOI: 10.4213/tvp299

 English version: Theory of Probability and its Applications, 2004, 48:1, 45–62

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