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Autoregressive processes and first-hit probabilities for randomized random walks

Published online by Cambridge University Press:  14 July 2016

Raisa Epstein Feldman
Raisa Epstein Feldman*
Affiliation:
University of California, Santa Barbara
*
∗Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA.
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Abstract

We find the first-hit distributions of symmetric randomized random walks on ℝ with exponential lifetime using prediction formulas for Gaussian stationary autoregressive processes, associated with the random walks.

Keywords

PREDICTIONSTATIONARY PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 347 - 359
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

This research was supported by ONR Grant No. N00014/89/J/1870.

References

Adler, R. J. and Epstein, R. (1987) Some central limit theorems for Markov paths and some properties of Gaussian random fields. Stoch. Proc. Appl. 24, 157–202.10.1016/0304-4149(87)90012-3Google Scholar
Blumenthal, R. M. and Getoor, R. K. (1968) Markov Processes and Potential Theory. Academic Press, New York.Google Scholar
Brockwell, P. J. and Davis, R. A. (1987) Time Series: Theory and Methods. Springer-Verlag, New York.10.1007/978-1-4899-0004-3Google Scholar
Dynkin, E. B. (1980) Markov processes and random fields. Bull. Amer. Math. Soc. 3, 975–999.10.1090/S0273-0979-1980-14831-4Google Scholar
Feldman, R. (1990) Exit distributions for Lévy processes via Gaussian techniques. Preprint.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. I. Wiley, New York.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. II. Wiley, New York.Google Scholar
Wampler, S. (1986) Missing values in time series analysis, Dept. of Statistics, Colorado State University.Google Scholar
Yaglom, A. M. (1962) An Introduction to the Theory of Stationary Random Functions. Prentice-Hall, Englewood Cliffs.Google Scholar
Ylvisaker, D. (1987) Prediction and design. Ann. Statist. 15, 1–19.10.1214/aos/1176350247Google Scholar