Strong solutions and strong Feller properties for regime-switching diffusion processes in an infinite state space

作者: Jinghai Shao

DOI:

关键词: Regime switchingDifferential equationStrong solutionsDiffusion (business)Mathematical analysisState spaceMathematicsUniqueness

摘要: We establish the existence and pathwise uniqueness of regime-switching diffusion processes in an infinite state space, which could be time-inhomogeneous state-dependent. Then strong Feller properties these are investigated by using theory parabolic differential equations dimensional-free Harnack inequalities.

参考文章(9)
Mark Pinsky, Ross G. Pinsky, Transience/Recurrence and Central Limit Theorem Behavior for Diffusions in Random Temporal Environments Annals of Probability. ,vol. 21, pp. 433- 452 ,(1993) , 10.1214/AOP/1176989410
Mrinal K. Ghosh, Aristotle Arapostathis, Steven I. Marcus, Optimal control of switching diffusions with application to flexible manufacturing systems Siam Journal on Control and Optimization. ,vol. 31, pp. 1183- 1204 ,(1993) , 10.1137/0331056
Martin Hairer, Bertrand Cloez, Exponential ergodicity for Markov processes with random switching arXiv: Probability. ,(2013) , 10.3150/13-BEJ577
Shizan Fang, Tusheng Zhang, A study of a class of stochastic differential equations with non-Lipschitzian coefficients Probability Theory and Related Fields. ,vol. 132, pp. 356- 390 ,(2005) , 10.1007/S00440-004-0398-Z
Z. Q. Chen, Z. Zhao, Potential theory for elliptic systems Annals of Probability. ,vol. 24, pp. 293- 319 ,(1996) , 10.1214/AOP/1042644718
Qingshuo Song, G. George Yin, Chao Zhu, Optimal Switching with Constraints and Utility Maximization of an Indivisible Market Siam Journal on Control and Optimization. ,vol. 50, pp. 629- 651 ,(2012) , 10.1137/10080823X
Feng-Yu Wang, Chenggui Yuan, Harnack inequalities for functional SDEs with multiplicative noise and applications Stochastic Processes and their Applications. ,vol. 121, pp. 2692- 2710 ,(2011) , 10.1016/J.SPA.2011.07.001