Year: 2006
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 125–140
Abstract
A class of implicit methods is introduced for Ito stochastic difference equations with Poisson-driven jumps. A convergence proof shows that these implicit methods share the same finite time strong convergence rate as the explicit Euler-Maruyama scheme. A mean-square linear stability analysis shows that implicitness offers benefits, and a natural analogue of mean-square A-stability is studied. Weak variants are also considered and their stability is analyzed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-IJNAM-893
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 125–140
Published online: 2006-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: A-stability backward Euler Euler-Maruyama linear stability Poisson process stochastic differential equation strong convergence theta method trapezoidal rule.