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On the Equivalence of Different Approaches to Stochastic Partial Differential Equations

โœ Scribed by G. Jetschke

Publisher
John Wiley and Sons
Year
1986
Tongue
English
Weight
612 KB
Volume
128
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

The solution of astochastic partial differential equation withwhite noise disturbance can be treated in two different ways: as & real-valued random field or as a function-space valued stochastic process. After introducing these views briefly it is shown that these two approaches m e equivalent. Some further results on FOURI~R decomposition and on asymptotic behaviour of the linear equation are given and a few comments on the nonlinear case are added.

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Let R be a compact region (Le., the closure of an open connected set) in R" which is of class C2. Let n i = l A = Zn,D, + a, be a first order partial differential expression on R, where D, = a/&,, ui is an m x m matrix of C2 functions, i = 1, \* \* \* , n, and a,, is an m x m matrix of C1 functions.