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Explicit formulae for stationary distributions of stress release processes

Part of: Markov processes Other natural sciences

Published online by Cambridge University Press:  14 July 2016

K. Borovkov  and
D. Vere-Jones
K. Borovkov*
Affiliation:
University of Melbourne
D. Vere-Jones*
Affiliation:
Victoria University of Wellington
*
∗Postal address: Department of Mathematics and Statistics, University of Melbourne, Parkville 3052, Australia. Email address: [email protected]
∗∗Postal address: School of Mathematical and Computer Sciences, Victoria University, PO Box 600, Wellington, New Zealand
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Abstract

Stress release processes are special Markov models attempting to describe the behaviour of stress and occurrence of earthquakes in seismic zones. The stress is built up linearly by tectonic forces and released spontaneously when earthquakes occur. Assuming that the risk is an exponential function of the stress, we derive closed form expressions for the stationary distribution of such processes, the moments of the risk, and the autocovariance function of the reciprocal risk process.

Keywords

Stress release modelsMarkov processesstationary distribution

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 92F05: Other natural sciences (should also be assigned at least one other classification number in section 92)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 315 - 321
Copyright
Copyright © by the Applied Probability Trust 2000 

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