Some analytic approximations for neutral stochastic functional differential equations (Q618045)
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scientific article; zbMATH DE number 5836660
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some analytic approximations for neutral stochastic functional differential equations |
scientific article; zbMATH DE number 5836660 |
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Some analytic approximations for neutral stochastic functional differential equations (English)
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14 January 2011
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An iterative sequence of approximate solutions is presented and proved to converge both with probability one and in the \(p\)th moment to the exact solution of the \(k\)-dimensional neutral stochastic functional differential equation \[ d[x(t)- G(x_t)]= a(t,x_t)\,dt+ b(t,x_t)\, dw_t,\quad t\in [t_0,T], \] where \(x_{t_0}= \xi= \{\xi(\theta): -\tau\leq\theta\leq 0\}\).
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neutral stochastic functional differential equation
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\(Z\)-algorithm
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approximate solutions
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convergence with probability one and in \(p\)th mean
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