Certain properties related to well posedness of switching diffusions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Dang Hai Nguyen¹  Yin, George¹  Zhu, Chao² 

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[2] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

关键词: Switching diffusion;    Continuous-state dependent switching;    Smoothness;    Feller property;   

DOI  :  10.1016/j.spa.2017.02.004

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free