Regime-switching diffusion processes: strong solutions and strong Feller property

  • 报告人: 张少钦 中央财经大学
  • 报告地址: 长江数学中心409报告厅
  • 报告时间: 5月13日 16:30--17:20
  • 主题摘要:
We investigate the existence and uniqueness of strong solutions up to an explosion time for state-dependent regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result is established under the general assumption that the diffusion in every fixed environment has a unique local strong solution. Under this assumption, we can extend recent results on the strong uniqueness of stochastic differential equations with singular coefficients to switching processes. Meanwhile, via Zvonkin's transformation, non-explosion conditions for regime-switching diffusion processes with integrable drift coefficients are given. The strong Feller property is proved by further assuming that the diffusion in every fixed environment generates a strong Feller semigroup, and our results can also be applied toirregular or degenerate situations.