Abstract
A stochastic parabolic equation on $[0,T]\times \mathbb{R}$ 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.
Highlights
In this paper we establish the averaging principle for the stochastic parabolic equationLuε(t, x)dt + f (t/ε, x, uε(t, x)) dt + σ (t/ε, x) dμ(x) = 0, uε(0, x) = u0(x), (1)where ε is a small positive parameter, (t, x) ∈ [0, T ] × R, μ is a general stochastic measure on Borel σ -algebra on R, f, σ are measurable functions, L is the operator of the form Lu(t, x) =∂ 2 u(t, a(t) ∂2x x) + ∂ u(t, b(t )∂x x) c(t )u(t, x) −
Where ε is a small positive parameter, (t, x) ∈ [0, T ] × R, μ is a general stochastic measure on Borel σ -algebra on R, f, σ are measurable functions, L is the operator of the form
The averaging principle for two-time-scales system driven by two independent Wiener processes was studied, for example, in [7]
Summary
In this paper we establish the averaging principle for the stochastic parabolic equation.
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