Occupation times sequences and martingales of simple random walks on the real line
DOI:
https://doi.org/10.4067/S0716-09172005000300002Keywords:
Occupation times, Simple random walks, Predictible compensators, First passage times, Optional sampling theorem, First order absolute moments.Abstract
Given a simple random walk on the real line, we consider the sequences of occupation times on states and associate to them martingales defined by the moments of first order of this random walk. We deduce by this way recurrent relations for the expectations of the occupation times in states before a given time, and then remarkable identities for the expectations of the absolute values of the random walk.
References
[1] F. Spitzer; Principles of Random Walk, Springer Verlag, New York, edición de (1976).
[2] H. Wilf; Generatingfunctionology, Academic Press, San Diego, (1994).
[3] M. Petrovsek, H. Wilf, D. Zeilberger; A=B, AK Peters, Wellesley, Massachusetts, (1996).
[4] P. Hoel, S. Port, Ch. Stone; Introduction to probabily theory, Houghton Mifflin Company, Boston, (1971).
[5] J. Neveu; Martingales à temps discret, Masson, Paris, (1972).
[6] E. Perkins; A global continous characterizaction of brownian local time, Annals of Probability 9, pp. 800 — 817, (1981).
[7] D. Dacunha-Castelle, M. Duflo; Probabilit´es et Statistiques, tomo 1, Masson, Paris, (1982).
[2] H. Wilf; Generatingfunctionology, Academic Press, San Diego, (1994).
[3] M. Petrovsek, H. Wilf, D. Zeilberger; A=B, AK Peters, Wellesley, Massachusetts, (1996).
[4] P. Hoel, S. Port, Ch. Stone; Introduction to probabily theory, Houghton Mifflin Company, Boston, (1971).
[5] J. Neveu; Martingales à temps discret, Masson, Paris, (1972).
[6] E. Perkins; A global continous characterizaction of brownian local time, Annals of Probability 9, pp. 800 — 817, (1981).
[7] D. Dacunha-Castelle, M. Duflo; Probabilit´es et Statistiques, tomo 1, Masson, Paris, (1982).
Published
2017-04-20
How to Cite
[1]
J. Lobo Segura, “Occupation times sequences and martingales of simple random walks on the real line”, Proyecciones (Antofagasta, On line), vol. 24, no. 3, pp. 205-227, Apr. 2017.
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