Articlegreen2000

Weak Approximations and Extrapolations of Stochastic Differential Equations with Jumps

52 citations0/0 files storedSIAM Journal on Numerical Analysis

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Stochastic processes and financial applications Numerical methods for differential equations Differential Equations and Numerical Methods

Abstract

Numerical discretization schemes are developed to approximate functionals of stochastic differential equations with jumps, and the convergence is shown to have an appropriate order. For the Euler scheme and the second order weak scheme, the leading coefficient of their global errors are determined by the stochastic Taylor expansion. Based on the error expression, the extrapolation technique can be applied to get a higher order convergence. Numerical examples are provided to compare various weak schemes and extrapolations.

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References

2016Numerical solution of stochastic differential equations 1996The law of the Euler scheme for stochastic differential equations 1997The Euler scheme for Lévy driven stochastic differential equations 1996The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density 1995Weak approximation of solutions of systems of stochastic differential equations 1986Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution 1988Time Discrete Taylor Approximations for Itǒ Processes with Jump Component

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