On the discretization in time of parabolic stochastic partial differential equations (Q5890275)
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scientific article; zbMATH DE number 1623590
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the discretization in time of parabolic stochastic partial differential equations |
scientific article; zbMATH DE number 1623590 |
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On the discretization in time of parabolic stochastic partial differential equations (English)
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9 March 2003
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parabolic stochastic partial differential equation
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Euler scheme
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stability
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evolution equation
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semi-discretization
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convergence
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The author studies an evolution equation of type NEWLINE\[NEWLINE du+(Au+f(u))dt = \sigma(u) dW, NEWLINE\]NEWLINE in a Hilbert space \(H\), with initial condition \(u(0)=u_0\in H\), where \(u\) is an \(H\)-valued random process, \(A\) an unbounded, nonnegative, self-adjoint operator on \(H\), and \(\{W(t)\}_{t\geq 0}\) a cylindrical Wiener process. Based on semi-discretization in time an Euler scheme is investigeted to approximate the solution. Questions of stability and convergence are studied under conditions of global and local Lipschitz continuity of the coefficients \(f\) and \(\sigma\).
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