Higher order spatial approximations for degenerate parabolic stochastic partial differential equations (Q2855121)
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scientific article; zbMATH DE number 6219416
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Higher order spatial approximations for degenerate parabolic stochastic partial differential equations |
scientific article; zbMATH DE number 6219416 |
Statements
24 October 2013
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Zakai equation
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nonlinear filtering
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Richardson's acceleration
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Euler implicit scheme
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Cauchy problem
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degenerate parabolic equation
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second-order stochastic parabolic partial differential equation
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convergence
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0.9123295
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0.90940154
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0.90057284
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0.8990637
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0.8981159
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0.8969601
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Higher order spatial approximations for degenerate parabolic stochastic partial differential equations (English)
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The Cauchy problem is considered for a second-order stochastic parabolic partial differential equation which is a generalization of the Zakai equation from nonlinear filtering theory. The parabolicity condition is allowed to be degenerate. An implicit finite difference scheme and its acceleration by Richardson's method are proposed for the approximate solution of the equation. The rate of convergence is investigated in the sup-norm. It is shown that the strong convergence rate can be accelerated to any order if the initial conditions, coefficients and free terms are smooth enough.
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