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On the moments of a self-correcting process

Published online by Cambridge University Press:  14 July 2016

D. Vere-Jones
Affiliation:
Victoria University of Wellington
Y. Ogata
Affiliation:
Institute of Statistical Mathematics, Tokyo

Abstract

The existence of ordinary and exponential moments of a point process with conditional intensity of the form is deduced from a Markov chain representation for t – ρN(t). These results form an application of recent theorems of Tweedie (1983a, b) and are used to obtain laws of large numbers for a range of functionals of the process.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1984 

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References

Billingsley, P. (1965) Ergodic Theory and Information. Wiley, New York.Google Scholar
Chung, K. L. (1967) Markov Chains with Stationary Transition Probabilities, 2nd edn. Springer-Verlag, Berlin.Google Scholar
Griffeath, D. (1975) A maximum coupling for Markov chains. Z. Wahrscheinlichkeitsth. 31, 95106.CrossRefGoogle Scholar
Isham, V. and Westcott, M. (1979) A self-correcting point process. Stoch. Proc. Appl. 8, 335347.CrossRefGoogle Scholar
Liptser, R. S. and Shiryaev, A. N. (1978) Statistics of Random Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Ogata, Y. and Vere-Jones, D. (1983) Inference for earthquake models: a self-correcting model. Stoch. Proc. Appl. Google Scholar
Tweedie, R. L. (1983a) Criteria for rates of convergence of Markov chains, with application to queuing and storage theory. David Kendall Festschrift. To appear.Google Scholar
Tweedie, R. L. (1983b) The existence of moments for stationary Markov chains. J. Appl. Prob. 20, 191196.CrossRefGoogle Scholar
Vere-Jones, D. (1978) Earthquake prediction — a statistician's view. J. Phys. Earth 26, 129146.CrossRefGoogle Scholar

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