Stability in distribution and stabilization of switching jump diffusions

Stability of numerical methods for jump diffusions and Markovian switching jump diffusions

This work is devoted to stability analysis of numerical solutions for jump diffusions and jump diffusions with Markovian switching. Different from the existing treatment of Euler-Maurayama methods for solutions of stochastic differential equations, we use techniques from stochastic approximation. We analyze the almost sure exponential stability and exponential pstability. Then Markovian regime-...

Numerical methods for controlled regime-switching diffusions and regime-switching jump diffusions

This work is concerned with numerical methods for controlled regime-switching diffusions, and regime-switching jump diffusions. Numerical procedures based on Markov chain approximation techniques are developed. Convergence of the algorithms is derived by means of weak convergence methods. In addition, examples are also provided for demonstration purpose. 2006 Elsevier Ltd. All rights reserved.

First Passage Time Moments of Jump-Diffusions with Markovian Switching

Jump-diffusions in Hilbert Spaces: Existence, Stability and Numerics

By means of an original approach, called “method of the moving frame”, we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path dependent coefficients driven by an infinite dimensional Wiener process and a compensated Poisson random measure. Our approach is based on a timedependent coordinate transform, w...

Numerical solutions for jump-diffusions with regime switching

This paper is devoted to numerical solutions for a class of jump-diffusions with regime switching. After briefly reviewing the notion of jump-diffusions with regime switching, finite-difference procedures are constructed. Under simple conditions, it is proved that the algorithm converges to the desired limit by means of a martingale problem formulation. Numerical experiments are carried out to ...