TY - JOUR
T1 - Convergence and Stability of Implicit Methods for Jump-Diffusion Systems
AU - D. J. Higham & P. E. Kloeden
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 - <p style="text-align: justify;">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.</p>