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arXiv · 1807.00363

On invariant probability measures of regime-switching diffusion processes with singular drifts

Shao-Qin Zhang
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Abstract

For regime-switching diffusions processes with singular drifts, we introduce integrability conditions involving a nice reference probability measure and the $Q$-matrix of the jump part to study the existence of the invariant probability measures. Consequently, the generator of the regime-switching diffusions process has an extension in the $L^1$-space w.r.t the invariant probability measure to be a generator of $C_0$-semigroup. Moreover, we prove the uniqueness of the extension. Regularities and the uniqueness of the invariant probability density w.r.t the nice reference probability measure are also considered.

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Shao-Qin Zhang. 2018-07-01. On invariant probability measures of regime-switching diffusion processes with singular drifts. https://arxiv.org/abs/1807.00363

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