SIAM Journal on Control and Optimization · 2015 · 59 citations · 17 references
EngineeringMathematicsPhysicsDynamical SystemsStochastic ProcessesBrownian MotionContinuous Dynamical SystemsDiffusion ProcessesMarkov ProcessesReaction-diffusion SystemsRegime-switching ModelsFeller ProcessesParabolic Partial Differential EquationsPathwise UniquenessState-space StructureStrong SolutionsTime-dependent DiffusionUniqueness In Parabolic Equations
We establish the existence and pathwise uniqueness of regime-switching diffusion processes in an infinite state space, which could be time-inhomogeneous and state-dependent. Then the strong Feller properties of these processes are investigated by using the theory of parabolic differential equations and dimensional-free Harnack inequalities.
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