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The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations

  • P.E. Kloeden (a1) and A. Neuenkirch (a2)

Abstract

The authors of this paper study approximation methods for stochastic differential equations, and point out a simple relation between the order of convergence in the pth mean and the order of convergence in the pathwise sense: Convergence in the pth mean of order α for all p ≥ 1 implies pathwise convergence of order α – ε for arbitrary ε > 0. The authors then apply this result to several one-step and multi-step approximation schemes for stochastic differential equations and stochastic delay differential equations. In addition, they give some numerical examples.

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References

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The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations

  • P.E. Kloeden (a1) and A. Neuenkirch (a2)

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