Averaging principle for the one-dimensional parabolic equation driven by stochastic measure

Abstract

A stochastic parabolic equation on [0, T ] × R driven by a general stochastic measure is considered. The averaging principle for the equation is established. The convergence rate is compared with other results on related topics.

Asymptotic properties of the parabolic equation driven by stochastic measure

“…and the same estimates hold for 24) and ( 23), we obtain (12); in (23) we can set, for example, A = 1.…”

“…Note that regularity of the solution was proved in [2], the solution's convergence in the case of integrator's convergence was proved in [18] and the averaging principle for such an equation was established in [12]. The asymptotic behavior of the moments of solutions of a stochastic differential system driven by a Brownian motion was considered in [5].…”

Transport equation driven by a stochastic measure

“…The recent results for the equations driven by stochastic measures may be found in [2], [9], [10]. The rest of the paper is organized as follows.…”