### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 14 |

ISBN (Print) | 0169-2690 |

Publication status | Published - 1999 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1486 |

ISSN (Print) | 0169-2690 |

### Keywords

- EWI-3306
- IR-65675
- METIS-141298
- MSC-60J80

### Cite this

*Families of birth-death processes with similar time-dependent behaviour*. (Memorandum / Department of Applied Mathematics; No. 1486). Enschede: University of Twente, Department of Applied Mathematics.

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*Families of birth-death processes with similar time-dependent behaviour*. Memorandum / Department of Applied Mathematics, no. 1486, University of Twente, Department of Applied Mathematics, Enschede.

**Families of birth-death processes with similar time-dependent behaviour.** / Lenin, R.B.; Parthasarathy, P.R.; Scheinhardt, Willem R.W.; van Doorn, Erik A.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Families of birth-death processes with similar time-dependent behaviour

AU - Lenin, R.B.

AU - Parthasarathy, P.R.

AU - Scheinhardt, Willem R.W.

AU - van Doorn, Erik A.

N1 - Imported from MEMORANDA

PY - 1999

Y1 - 1999

N2 - We consider birth-death processes taking values in ${\cal N} \equiv \{0,1,\ldots\}$, but allow the death rate in state $0$ to be positive, so that escape from ${\cal N}$ is possible. Two such processes with transition functions $\{p_{ij}(t)\}$ and $\{{\tilde p}_{ij}(t)\}$ are said to be {\it similar} if, for all $i,j \in {\cal N},$ there are constants $c_{ij}$ such that ${\tilde p}_{ij}(t) = c_{ij}p_{ij}(t)$ for all $t \geq 0.$ We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family.

AB - We consider birth-death processes taking values in ${\cal N} \equiv \{0,1,\ldots\}$, but allow the death rate in state $0$ to be positive, so that escape from ${\cal N}$ is possible. Two such processes with transition functions $\{p_{ij}(t)\}$ and $\{{\tilde p}_{ij}(t)\}$ are said to be {\it similar} if, for all $i,j \in {\cal N},$ there are constants $c_{ij}$ such that ${\tilde p}_{ij}(t) = c_{ij}p_{ij}(t)$ for all $t \geq 0.$ We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family.

KW - EWI-3306

KW - IR-65675

KW - METIS-141298

KW - MSC-60J80

M3 - Report

SN - 0169-2690

T3 - Memorandum / Department of Applied Mathematics

BT - Families of birth-death processes with similar time-dependent behaviour

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -