COMPARISON FOR SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE

Title & Authors
COMPARISON FOR SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE
CHO, NHAN-SOOK;

Abstract
We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $\small{Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,}$ $\small{where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\small{\beta^1\leq\beta^2\;then\;u^1{\leq}u^2}$ under some conditions.
Keywords
comparison theorem;SPDE;martingale measure;
Language
English
Cited by
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