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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.24 no.3 Antofagasta Dec. 2005

http://dx.doi.org/10.4067/S0716-09172005000300002 

 

Proyecciones
Vol. 24, No 3, pp. 205-227, December 2005.
Universidad Católica del Norte

Antofagasta - Chile

 

OCCUPATION TIMES SEQUENCES AND MARTINGALES OF SIMPLE RANDOM WALKS ON THE REAL LINE

 

JAIME LOBO

Universidad de Costa Rica, Costa Rica


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.

Key words : occupation times; simple random walks; predictible compensators; first passage times ; optional sampling theorem; first order absolute moments.

 

References

[1] F. Spitzer; Principles of Random Walk, Springer Verlag, New York, edición de (1976).         [ Links ]

[2] H. Wilf; Generatingfunctionology, Academic Press, San Diego, (1994).         [ Links ]

[3] M. Petrovsek, H. Wilf, D. Zeilberger; A=B, AK Peters, Wellesley, Massachusetts, (1996).         [ Links ]

[4] P. Hoel, S. Port, Ch. Stone; Introduction to probabily theory, Houghton Mifflin Company, Boston, (1971).         [ Links ]

[5] J. Neveu; Martingales à temps discret, Masson, Paris, (1972).         [ Links ]

[6] E. Perkins; A global continous characterizaction of brownian local time, Annals of Probability 9, pp. 800 — 817, (1981).         [ Links ]

[7] D. Dacunha-Castelle, M. Duflo; Probabilités et Statistiques, tomo 1, Masson, Paris, (1982).         [ Links ]

 

Jaime Lobo Segura
Centro de Investigaciones en Matemática Pura y Aplicada
(CIMPA)
Universidad de Costa Rica
San José
Costa Rica
e-mail : jaimelobosegura@hotmail.com

Received : August 2005. Accepted : November 2005

 

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