Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T14:44:31.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Intertwined Markov processes: the extended Chapman–Kolmogorov equation

Part of: Partial differential operators Markov processes Abstract harmonic analysis Functional-differential and differential-difference equations Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  04 September 2017

Wha-Suck Lee  and
Niko Sauer
Wha-Suck Lee
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield 0028, Pretoria, South Africa ([email protected]; [email protected])
Niko Sauer
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield 0028, Pretoria, South Africa ([email protected]; [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Uniformization transforms a pseudo-Poisson process with unequal intensities (leaving rates) into one with uniform intensity. Self-transitions is the price to pay. Two intensities arise when one considers an absorbing barrier of a Markov process as a body in its own right: a pair of Markov processes intertwined by an extended Chapman–Kolmogorov equation naturally arises. We show that Sauer's two-state space empathy theory handles such intertwined processes. The price of self-transitions is also avoided.

Keywords

Chapman–Kolmogorov equationintertwined Markov processesempathyimplicitB-evolution equationpseudo-Poisson processFokker–Planck equations

MSC classification

Secondary: 47D07: Markov semigroups and applications to diffusion processes 47F99: None of the above, but in this section 60J27: Continuous-time Markov processes on discrete state spaces 60J99: None of the above, but in this section 60J28: Applications of continuous-time Markov processes on discrete state spaces 60J35: Transition functions, generators and resolvents 34K32: Implicit equations 34K30: Equations in abstract spaces 47D03: Groups and semigroups of linear operators 47D99: None of the above, but in this section 43A05: Measures on groups and semigroups, etc.
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 1 , February 2018 , pp. 123 - 131
Copyright
Copyright © Royal Society of Edinburgh 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)