### Abstract

Original language | English |
---|---|

Pages (from-to) | 351-366 |

Number of pages | 15 |

Journal | Probability in the engineering and informational sciences |

Volume | 16 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 |

### Fingerprint

### Keywords

- Birth-death process
- ergodic Markov chain
- deviation matrix
- convergence to stationarity
- IR-62339
- EWI-12837
- METIS-206668

### Cite this

*Probability in the engineering and informational sciences*,

*16*(3), 351-366. https://doi.org/10.1017/S0269964802163066

}

*Probability in the engineering and informational sciences*, vol. 16, no. 3, pp. 351-366. https://doi.org/10.1017/S0269964802163066

**The deviation matrix of a continuous-time Markov chain.** / Coolen-Schrijner, Pauline; van Doorn, Erik A.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - The deviation matrix of a continuous-time Markov chain

AU - Coolen-Schrijner, Pauline

AU - van Doorn, Erik A.

PY - 2002

Y1 - 2002

N2 - he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\Pi$ is the matrix $D \equiv \int_0^{\infty} (P(t)-\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a birth-death process is investigated in detail. We also describe a new application of deviation matrices by showing that a measure for the convergence to stationarity of a stochastically increasing Markov chain can be expressed in terms of the elements of the deviation matrix of the chain.

AB - he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\Pi$ is the matrix $D \equiv \int_0^{\infty} (P(t)-\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a birth-death process is investigated in detail. We also describe a new application of deviation matrices by showing that a measure for the convergence to stationarity of a stochastically increasing Markov chain can be expressed in terms of the elements of the deviation matrix of the chain.

KW - Birth-death process

KW - ergodic Markov chain

KW - deviation matrix

KW - convergence to stationarity

KW - IR-62339

KW - EWI-12837

KW - METIS-206668

U2 - 10.1017/S0269964802163066

DO - 10.1017/S0269964802163066

M3 - Article

VL - 16

SP - 351

EP - 366

JO - Probability in the engineering and informational sciences

JF - Probability in the engineering and informational sciences

SN - 0269-9648

IS - 3

ER -