TY - JOUR T1 - Convergence and Stability of Implicit Methods for Jump-Diffusion Systems JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 125 EP - 140 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/893.html KW - A-stability, backward Euler, Euler-Maruyama, linear stability, Poisson process, stochastic differential equation, strong convergence, theta method, trapezoidal rule. AB -

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.