Smoluchowski–Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension

被引：1
作者：
Michael Salins
机构：
[1] Boston University,
来源：
Stochastics and Partial Differential Equations: Analysis and Computations | 2019年 / 7卷
关键词：
Smoluchowski–Kramers approximation; Stochastic wave equation; Stochastic heat equation; Stochastic partial Differential equations; 60H15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show that the solutions to the damped stochastic wave equation converge pathwise to the solution of a stochastic heat equation. This is called the Smoluchowski–Kramers approximation. Cerrai and Freidlin have previously demonstrated that this result holds in the cases where the system is exposed to additive noise in any spatial dimension or when the system is exposed to multiplicative noise and the spatial dimension is one. The current paper proves that the Smoluchowski–Kramers approximation is valid in any spatial dimension when the system is exposed to multiplicative noise.
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页码：86 / 122
页数：36
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