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The discrete uhlenbeck–ornstein process

Published online by Cambridge University Press:  14 July 2016

Eric Renshaw
Eric Renshaw*
Affiliation:
University of Edinburgh
*
∗ Postal address: Department of Statistics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK.
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Abstract

A correlated random walk is studied in which, at each stage, the velocity changes according to a first-order process. Motion is considered both with and without friction, the former situation being the discrete analogy of the Uhlenbeck–Ornstein process. Exact and limiting expressions are developed for the cumulant structures.

Keywords

CORRELATED RANDOM WALKVELOCITYFRICTIONCUMULANTSPARTITIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 908 - 917
Copyright
Copyright © Applied Probability Trust 1987 

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References

Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Andrews, G. E. (1976) The Theory of Partitions (Encyclopedia of Mathematics and its Applications, Vol. 2, ed. Rota, Gian-Carlo). Addison-Wesley, Reading, Massachusetts.Google Scholar
Gillis, J. (1955) Correlated random walk. Proc. Camb. Phil. Soc. 51, 639–651.CrossRefGoogle Scholar
Goldstein, S. (1951) On diffusion by discontinuous movements, and on the telegraph equation. Quart. J. Mech. 4, 129–156.Google Scholar
Gradshteyn, I. S. and Rhyzik, I. M. (1965) Tables of Integrals, Series and Products , 4th edn. Academic Press, London.Google Scholar
Hardy, G. H. and Wright, E. M. (1979) An Introduction to the Theory of Numbers, 5th edn. Clarendon Press, Oxford.Google Scholar
Iossif, G. (1986) Return probabilities for correlated random walks. J. Appl. Prob. 23, 201–207.Google Scholar
Jakeman, E. and Hoenders, B. J. (1982) Scattering by a random surface of rectangular grooves. Optica Acta 29, 1587–1598.Google Scholar
Renshaw, E. and Henderson, R. (1981) The correlated random walk. J. Appl. Prob. 18, 403–414.CrossRefGoogle Scholar
Uhlenbeck, G. E. and Ornstein, L. S. (1930) On the theory of Brownian motion. Phys. Rev. 36, 823–841.Google Scholar