The Burgers equation driven by a stochastic measure

Abstract

The class of one-dimensional equations driven by a stochastic measure μ is studied. For μ only σ-additivity in probability is assumed. This class of equations includes the Burgers equation and the heat equation. The existence and uniqueness of the solution are proved, and the averaging principle for the equation is studied.

Keywords

• Stochastic Burgers equation
• stochastic heat equation
• Stochastic measure
• mild solution
• Averaging principle