Pathwise stability of degenerate stochastic evolutions (Q621797)
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scientific article; zbMATH DE number 5842774
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pathwise stability of degenerate stochastic evolutions |
scientific article; zbMATH DE number 5842774 |
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Pathwise stability of degenerate stochastic evolutions (English)
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28 January 2011
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The author proves upper bounds for the almost sure exponential growth rate of the solution of a class of linear stochastic differential equations taking values in a Hilbert space. The key idea is to find a Lyapunov type functional via an associated operator equation. The results can -- in particular -- be used to provide sufficient conditions for almost sure asymptotic stability. The author applies the results to the stochastic heat equation and to one-dimensional stochastic delay differential equations.
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stochastic evolution equation
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exponential growth rate
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Lyapunov exponent
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pathwise stability
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stochastic delay differential equation
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