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ON IDENTITIES FOR A RANDOM WALK IN AN ORTHANT WITH ABSORBING BOUNDARY

Published online by Cambridge University Press:  06 June 2003

Leendert A. Klein Haneveld
Leendert A. Klein Haneveld
Affiliation:
Hogeschool van Amsterdam, Gouden Leeuw 344, 1103 KH Amsterdam, The Netherlands, E-mail: [email protected], [email protected]
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Abstract

For a left-continuous random walk in an orthant with absorbing boundary, the generating function of the transition probabilities is determined by a well-known functional equation. We give a simple probabilistic derivation of this functional equation, which simultaneously proves the hitting point identity and Wald's exponential identity for the absorption time.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 17 , Issue 3 , July 2003 , pp. 411 - 415
Copyright
© 2003 Cambridge University Press

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