A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems

被引：18
|
作者：
Bect, Julien [1 ]
机构：
[1] Supelec, Dept Signal Proc & Elect Syst, Gif Sur Yvette, France
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2010年 / 4卷 / 02期
关键词：
Stochastic hybrid systems; Stochastic system with jumps; Markov processes; Fokker-Planck equation; DIFFUSION; MODEL;
D O I：
10.1016/j.nahs.2009.07.008
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A general formulation of the Fokker-Planck-Kolmogorov (FPK) equation for stochastic hybrid systems is presented, within the framework of Generalized Stochastic Hybrid Systems (GSHSs). The FPK equation describes the time evolution of the probability law of the hybrid state. Our derivation is based on the concept of mean jump intensity, which is related to both the usual stochastic intensity (in the case of spontaneous jumps) and the notion of probability current (in the case of forced jumps). This work unifies all previously known instances of the FPK equation for stochastic hybrid systems, and provides GSHS practitioners with a tool to derive the correct evolution equation for the probability law of the state in any given example. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：357 / 370
页数：14
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