1. APPROXIMATION METHODS FOR HYBRID DIFFUSION SYSTEMS WITH STATE-DEPENDENT SWITCHING PROCESSES: NUMERICAL ALGORITHMS AND EXISTENCE AND UNIQUENESS OF SOLUTIONS.
- Author
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YIN, G., XUERONG MAO, CHENGGUI YUAN, and DINGZHOU CAO
- Subjects
- *
DIFFUSION processes , *CONTINUOUS geometries , *STOCHASTIC differential equations , *ALGORITHMS , *STOCHASTIC convergence - Abstract
Focusing on hybrid diffusions in which continuous dynamics and discrete events coexist, this work is concerned with approximation of solutions for hybrid stochastic differential equations with a state-dependent switching process. Iterative algorithms are developed. The continuous-state-dependent switching process presents added difficulties in analyzing the numerical procedures. Weak convergence of the algorithms is established by a martingale problem formulation first. This weak convergence result is then used as a bridge to obtain strong convergence. In this process, the existence and uniqueness of the solution of the switching diffusions with continuous-state-dependent switching are obtained. In contrast to existing results of solutions of stochastic differential equations in which the Picard iterations are utilized, Euler's numerical schemes are considered here. Moreover, decreasing-stepsize algorithms together with their weak convergence are given. Numerical experiments are also provided for demonstration. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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