Volume 3, Issue 2
Convergence and Stability of Implicit Methods for Jump-diffusion Systems

D. J. Higham and P. E. Kloeden

Int. J. Numer. Anal. Mod., 3 (2006), pp. 125-140

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  • 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 analyzed.

  • History

Published online: 2006-03

  • AMS Subject Headings

65C30, 65L20, 60H10

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