Articlegreen2015

Strong Solutions and Strong Feller Properties for Regime-Switching Diffusion Processes in An Infinite State Space

56 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Stochastic processes and statistical mechanics

Abstract

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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References

2010Hybrid Switching Diffusions: Properties and Applications 2005Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering 2005A study of a class of stochastic differential equations with non-Lipschitzian coefficients

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2017On Feller and Strong Feller Properties and Exponential Ergodicity of Regime-Switching Jump Diffusion Processes with Countable Regimes 2018Invariant Measures and Euler--Maruyama's Approximations of State-Dependent Regime-Switching Diffusions

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