An existenc theorem for a stochastic partial differential equation arising from filtering theory (Q761697)
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scientific article; zbMATH DE number 3888635
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existenc theorem for a stochastic partial differential equation arising from filtering theory |
scientific article; zbMATH DE number 3888635 |
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An existenc theorem for a stochastic partial differential equation arising from filtering theory (English)
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1984
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The Cauchy problem for the following stochastic partial differential equation \[ du(t,x)=u_{xx}(t,x)dt+h(x)u(t,x)dw_ t,\quad u(0,x)=u_ 0(x) \] where h is any polynomial of degree n and w is a real Wiener process, is investigated. The method consists in performing a transformation of the problem by \[ v(t,x)=\exp [-h(x)w(t)]u(t,x) \] to get a deterministic equation w.p. 1 with respect to v(t,x).
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Cauchy problem
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0.91615236
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0.91615236
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0.91074276
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0.90848184
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0.9061094
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