Theory of Probability and Mathematical Statistics
The Burgers-type equation driven by a stochastic measure
Vadym Radchenko
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Abstract: We study the one-dimensional equation driven by a stochastic measure μ. For μ we assume only σ-additivity in probability. Our results imply the global existence and uniqueness of the solution to the heat equation and the local existence and uniqueness of the solution to the Burgers equation. The averaging principle for such equation is studied.
Keywords: Stochastic Burgers equation, stochastic heat equation, stochastic measure, mild solution, averaging principle
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