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Integral functionals under the excursion measure

Part of: Markov processes

Published online by Cambridge University Press:  04 May 2020

Maciej Wiśniewolski
Maciej Wiśniewolski*
Affiliation:
University of Warsaw
*
*Postal address: Institute of Mathematics, University of Warsaw Banacha 2, 02-097 Warszawa, Poland. Email address: [email protected].
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Abstract

A new approach to the problem of finding the distribution of integral functionals under the excursion measure is presented. It is based on the technique of excursion straddling a time, stochastic analysis, and calculus on local time, and it is done for Brownian motion with drift reflecting at 0, and under some additional assumptions for some class of Itó diffusions. The new method is an alternative to the classical potential-theoretic approach and gives new specific formulas for distributions under the excursion measure.

Keywords

Brownian motion with driftexcursions of Markov processexcursion measurefirst hitting time of 0Itó diffusion

MSC classification

Primary: 60J45: Probabilistic potential theory
Secondary: 60J55: Local time and additive functionals 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 1 , March 2020 , pp. 137 - 155
Copyright
© Applied Probability Trust 2020

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