Optimal global approximation of stochastic differential equations with additive Poisson noise (Q329304)
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scientific article; zbMATH DE number 6642163
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal global approximation of stochastic differential equations with additive Poisson noise |
scientific article; zbMATH DE number 6642163 |
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Optimal global approximation of stochastic differential equations with additive Poisson noise (English)
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21 October 2016
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Lower bounds on error are derived for strong global approximations of the scalar stochastic differential equation \[ dX(t)=a(t,X(t))dt+c(t)dN(t),\quad t\in[0,T],\quad X(0)=x_0, \] where \(N\) is a homogeneous Poisson process. Asymptomatically optimal schemes based on the Euler method are constructed. It is shown that when \(N\) is additive Poisson noise, applying adaptive, rather than regular, step-size control to discretize the interval \([0,T]\) yields more efficient schemes.
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stochastic differential equations with jumps
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Poisson process
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minimal strong error
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step-size control
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asymptotically optimal algorithm
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error bound
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Euler method
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