A Lax equivalence theorem for stochastic differential equations (Q989145)
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scientific article; zbMATH DE number 5775772
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Lax equivalence theorem for stochastic differential equations |
scientific article; zbMATH DE number 5775772 |
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A Lax equivalence theorem for stochastic differential equations (English)
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27 August 2010
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Consistency, numerical stability, and convergence are defined in the mean square sense for numerical methods for approximating solutions of a class of stochastic partial differential equations. It is then proved that a consistent method is convergent if and only if it is stable. An example is given in which this result is applied to Euler-Maruyama and to Milstein method approximations of a stochastic heat equation with multiplicative noise.
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stochastic partial differential equations
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Lax equivalence theorem
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numerical approximation
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consistency
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stability
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convergence
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