Smoluchowski–Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension
Files
Published version
Date
2019-03
Authors
Salins, Michael
Version
Published version
OA Version
Citation
Michael Salins. 2019. "Smoluchowski–Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension." Stochastics and Partial Differential Equations: Analysis and Computations, Volume 7, Issue 1, pp. 86 - 122. https://doi.org/10.1007/s40072-018-0123-z
Abstract
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.