A duality relation for entrance and exit laws for Markov processes

J. Theodore Cox, Uwe Rösler

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

Markov processes Xt on (X, FX) and Yt on (Y, FY) are said to be dual with respect to the function f(x, y) if Exf(Xt, y) = Eyf(x, Yt for all x ε{lunate} X, y ε{lunate} Y, t ≥ 0. It is shown that this duality reverses the role of entrance and exit laws for the processes, and that two previously published results of the authors are dual in precisely this sense. The duality relation for the function f(x, y) = 1{x<y} is established for one-dimensional diffusions, and several new results on entrance and exit laws for diffusions, birth-death processes, and discrete time birth-death chains are obtained.

Original languageEnglish (US)
Pages (from-to)141-156
Number of pages16
JournalStochastic Processes and their Applications
Volume16
Issue number2
DOIs
StatePublished - Feb 1984

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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