The Annals of Applied Probability

The Equivalence of the Cox Process with Squared Radial Ornstein-Uhlenbeck Intensity and the Death Process in a Simple Population Model

Peter Clifford and Gang Wei

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Abstract

Two kinds of stationary point process are considered. One is generated by the sequence of death times in a simple immigration, birth and death process; the other is the Cox process with intensity given by the square of the radial Ornstein-Uhlenbeck process. By comparison of the coincidence densities, we show that the two classes of processes are equivalent. An explicit expression is given for the coincidence density of arbitrary order.

Article information

Source
Ann. Appl. Probab. Volume 3, Number 3 (1993), 863-873.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1177005368

Digital Object Identifier
doi:10.1214/aoap/1177005368

Mathematical Reviews number (MathSciNet)
MR1233630

Zentralblatt MATH identifier
0784.60029

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E10: Characterization and structure theory 62G05: Estimation 60G15: Gaussian processes 60G55: Point processes

Keywords
Cox process birth death and immigration Ornstein-Uhlenbeck point process

Citation

Clifford, Peter; Wei, Gang. The Equivalence of the Cox Process with Squared Radial Ornstein-Uhlenbeck Intensity and the Death Process in a Simple Population Model. Ann. Appl. Probab. 3 (1993), no. 3, 863--873. doi:10.1214/aoap/1177005368. http://projecteuclid.org/euclid.aoap/1177005368.


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