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Quasi-Stationary Distributions, Eigenmeasures, and Eigenfunctions of Markov Processes

  • Joseph Glover
Part of the Progress in Probability and Statistics book series (PRPR, volume 9)

Abstract

Let Pt be a submarkov semigroup on a Lusin topological state space E with Borel field E. We call a positive sigma-finite measure m on E an eigenmeasure if mPt = e-ct m for some real number c. We call a positive E-measurable function f an eigenfunction if ptf = e-ctf for some real number c. In each case, we call c the eigenvalue of either the eigenmeasure or the eigenfunction. Eigenmeasures are also known by the name quasi-stationary distributions in the Markov chain literature: see [5], [17], [18].

Keywords

Potential Density Semi Group Resolvent Equation Discrete State Space Excessive Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • Joseph Glover
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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