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On evaluations and asymptotic approximations of first-passage-time probabilities

Published online by Cambridge University Press:  01 July 2016

L. Sacerdote*
Affiliation:
Università di Torino
F. Tomassetti*
Affiliation:
Universita di Napoli
*
* Postal address: Dipartimento di Matematica, Universita di Torino, Via Carlo Alberto 10, 10123 Torino, Italy.
** Postal address: Dipartimento di Matematica e Applicazioni, Universita di Napoli, Via Cintia, 80126 Napoli, Italy.

Abstract

The series expansion for the solution of the integral equation for the first-passage-time probability density function, obtained by resorting to the fixed point theorem, is used to achieve approximate evaluations for which error bounds are indicated. A different use of the fixed point theorem is then made to determine lower and upper bounds for asymptotic approximations, and to examine their range of validity.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Research carried out under C.N.R. contracts and under M.U.R.S.T. financial support.

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