Certain properties related to well posedness of switching diffusions |
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Authors: | Dang Hai Nguyen George Yin Chao Zhu |
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Affiliation: | 1. Department of Mathematics, Wayne State University, Detroit, MI 48202, United States;2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, United States |
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Abstract: | This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions, in the setup, the discrete component (the switching) depends on the continuous component (the diffusion process). The objective of this paper is to provide a number of properties related to the well posedness. First, the differentiability with respect to initial data of the continuous component is established. Then, further properties including uniform continuity with respect to initial data, and smoothness of certain functionals are obtained. Moreover, Feller property is obtained under only local Lipschitz continuity. Finally, an example of Lotka–Volterra model under regime switching is provided as an illustration. |
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Keywords: | 60J05 60J60 Switching diffusion Continuous-state dependent switching Smoothness Feller property |
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