## 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 language | English |
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Pages (from-to) | 372-393 |

Number of pages | 22 |

Journal | Journal of Applied Probability |

Volume | 58 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2021 |

### Bibliographical note

Accepted author manuscript## Keywords

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