Convergence and Stability of Implicit Methods for Jump-Diffusion Systems

Convergence and Stability of Implicit Methods for Jump-Diffusion Systems

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.