# American Institute of Mathematical Sciences

January  2008, 9(1): 47-64. doi: 10.3934/dcdsb.2008.9.47

## Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes

 1 Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, United Kingdom 2 Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, Scotland, United Kingdom

Received  December 2006 Revised  June 2007 Published  October 2007

Stochastic differential equations with Poisson driven jumps of random magnitude are popular as models in mathematical finance. Strong, or pathwise, simulation of these models is required in various settings and long time stability is desirable to control error growth. Here, we examine strong convergence and mean-square stability of a class of implicit numerical methods, proving both positive and negative results. The analysis is backed up with numerical experiments.
Citation: Graeme D. Chalmers, Desmond J. Higham. Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 47-64. doi: 10.3934/dcdsb.2008.9.47
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