Approximation of Invariant Measures for Regime-switching Diffusions

• DOI: 10.1007/s11118-015-9526-x
• Publication Date: 2015-12-16T01:13:33Z
• Authors: Jianhai Bao; Jinghai Shao; Chenggui Yuan
• Keywords: Potential theory; Wasserstein Metric

22 pages<br/>In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with a range of regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for regime-switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the "averaging condition" holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for regime-switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.<br/>