Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems (extended version)

Abstract : A general formulation of the Fokker-Planck-Kolmogorov (FPK) equation for stochastic hybrid systems is presented, within the framework of Generalized Stochastic Hybrid Systems (GSHS). 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.
Complete list of metadatas

https://hal-supelec.archives-ouvertes.fr/hal-00350046
Contributor : Julien Bect <>
Submitted on : Tuesday, January 6, 2009 - 9:07:04 AM
Last modification on : Monday, December 14, 2020 - 12:38:04 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 6:33:36 PM

Files

Bect-NAHS.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00350046, version 1
  • ARXIV : 0901.0615

Citation

Julien Bect. A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems (extended version). 2009. ⟨hal-00350046v1⟩

Share

Metrics

Record views

11

Files downloads

144