COMPARISON FOR SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE

CHO, NHAN-SOOK

doi:10.4134/BKMS.2005.42.2.231

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COMPARISON FOR SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE

Journal title : Bulletin of the Korean Mathematical Society
Volume 42, Issue 2, 2005, pp.231-244
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2005.42.2.231

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. ${$$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$}$ ${$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 ${$\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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