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Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations

Published online by Cambridge University Press:  20 November 2018

Tokuzo Shiga
Tokuzo Shiga*
Affiliation:
Department of Applied Physics Tokyo Institute of Technology Oh-okayama, Meguro Tokyo 152 Japan
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Abstract

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The paper is concerned with the comparison of two solutions for a one-dimensional stochastic partial differential equation. Noting that support compactness of solutions propagates with passage of time, we define the SCP property and show that the SCP property and the strong positivity are two contrasting properties of solutions for one-dimensional SPDEs, which are due to degeneracy of the noise-term coefficient

Keywords

60H15SPDEcompact support propertystrong comparison theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 415 - 437
Copyright
Copyright © Canadian Mathematical Society 1994

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