Properties of solutions of stochastic differential equations with continuous-state-dependent switching |
| |
Authors: | G Yin C Zhu |
| |
Institution: | a Department of Mathematics, Wayne State University, Detroit, MI 48202, United States b Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, United States |
| |
Abstract: | This work is concerned with several properties of solutions of stochastic differential equations arising from hybrid switching diffusions. The word “hybrid” highlights the coexistence of continuous dynamics and discrete events. The underlying process has two components. One component describes the continuous dynamics, whereas the other is a switching process representing discrete events. One of the main features is the switching component depending on the continuous dynamics. In this paper, weak continuity is proved first. Then continuous and smooth dependence on initial data are demonstrated. In addition, it is shown that certain functions of the solutions verify a system of Kolmogorov's backward differential equations. Moreover, rates of convergence of numerical approximation algorithms are dealt with. |
| |
Keywords: | 60J05 60J60 |
本文献已被 ScienceDirect 等数据库收录! |
|