Fubao Xi

Stability of Regime-Switching Jump Diffusions

This work is concerned with the stability of a class of switching jump-diffusion processes. The processes under consideration can be thought of as a number of jump-diffusion processes modulated by a random switching device. The motivation of our study stems from a wide range of applications in communication systems, flexible manufacturing and production planning, financial engineering, and economics. A distinct feature of the two-component process

Stability and Recurrence of Regime-Switching Diffusion Processes

(X(t),\alpha(t))

Stability for a random evolution equation with Gaussian perturbation

considered in this paper is that the switching process

Numerical solutions of regime-switching jump diffusions

\alpha(t)

STATIONARY SOLUTION FOR A STOCHASTIC LIÉNARD EQUATION WITH MARKOVIAN SWITCHING

depends on the

Asymptotic properties of nonlinear autoregressive Markov processes with state-dependent switching

X(t)

On Feller and Strong Feller Properties and Exponential Ergodicity of Regime-Switching Jump Diffusion Processes with Countable Regimes

process. This paper focuses on the long-time behavior, namely, stability of the switching jump diffusions. First, the definitions of regularity and stability are recalled. Next it is shown that under suitable conditions, the underlying systems are regular or have no finite explosion time. To study stability of the trivial solution (or the equilibrium point 0), systems that are linearizable (in the

Coupling and Exponential Convergence Rate for Markovian Switching Jump Diffusions

x

Stochastic Liénard Equations with Random Switching and Two-time Scales

variable) in a neighborhood of 0 are considered. Sufficient conditions for stability and instability are obtained. Then, almost sure stability is examined by treating a Lyapunov exponent. The stability conditions present a gap for stability and instability owing to the maximum and minimal eigenvalues associated with the drift and diffusion coefficients. To close the gap, a transformation technique is used to obtain a necessary and sufficient condition for stability.

Removing logarithms in Poisson approximation to the partial sum process of a Markov chain

We provide some criteria on the stability of regime-switching diffusion processes. Both the state-independent and state-dependent regime-switching diffusion processes with switching in a finite state space and an infinite countable state space are studied in this work. We provide two methods to deal with switching processes in an infinite countable state space. One is a finite partition method based on the nonsingular M-matrix theory. Another is an application of principal eigenvalue of a bilinear form. Our methods can deal with both linear and nonlinear regime-switching diffusion processes. Moreover, the method of principal eigenvalue is also used to study the recurrence of regime-switching diffusion processes.