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

Part of: Stochastic processes Distribution theory Markov processes

Published online by Cambridge University Press:  01 July 2016

L. Sacerdote  and
F. Tomassetti
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.
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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.

Keywords

FIRST-PASSAGE-TIMEDIFFUSION PROCESSESORSTEIN-UHLENBECK PROCESSESFELLER PROCESSES

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60J60: Diffusion processes 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 62E17: Approximations to distributions (nonasymptotic)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 270 - 284
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.

References

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