Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

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Abstract

Our aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox-Ingersoll-Ross process.

Original languageEnglish
Pages (from-to)372-393
Number of pages22
JournalJournal of Applied Probability
Volume58
Issue number2
DOIs
Publication statusPublished - 2021

Keywords

  • diffusion limit
  • Markov chain
  • Markov modulation
  • regime switching
  • state occupation measure
  • stochastic integral

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