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Stochastic processes directed by randomized time

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Mei-Ling Ting Lee  and
G. Alex Whitmore
Mei-Ling Ting Lee*
Affiliation:
Harvard University
G. Alex Whitmore*
Affiliation:
McGill University
*
∗ Present address: Department of Statistics, Harvard University, 1 Oxford St. Cambridge, MA 02138, USA.
∗∗∗ Postal address: Faculty of Management, McGill University, 1001 Sherbrooke St West, Montreal, Quebec H3A 1G5, Canada.
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Abstract

The paper investigates stochastic processes directed by a randomized time process. A new family of directing processes called Hougaard processes is introduced. Monotonicity properties preserved under subordination, and dependence among processes directed by a common randomized time are studied. Results for processes subordinated to Poisson and stable processes are presented. Potential applications to shock models and threshold models are also discussed. Only Markov processes are considered.

Keywords

CLUSTERINGDEPENDENCEGAMMAHOUGAARDINVERSE GAUSSIANMARKOVPOISSONSHOCK MODELSSTABLESUBORDINATIONTHRESHOLD MODELSTOTAL POSITIVITY

MSC classification

Primary: 60G07: General theory of processes
Secondary: 60G55: Point processes 60E07: Infinitely divisible distributions; stable distributions

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 302 - 314
Copyright
Copyright © Applied Probability Trust 1993 

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