Certain properties related to well posedness of switching diffusions

Dang Hai Nguyen, George Yin and Chao Zhu

Stochastic Processes and their Applications, 2017, vol. 127, issue 10, 3135-3158

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.

Keywords: Switching diffusion; Continuous-state dependent switching; Smoothness; Feller property (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:10:p:3135-3158

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DOI: 10.1016/j.spa.2017.02.004

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