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A remark on positive sojourn times of symmetric processes

Part of: Limit theorems Markov processes Distribution theory - Probability

Published online by Cambridge University Press:  28 March 2018

Christophe Profeta
Christophe Profeta*
Affiliation:
Université d'Évry-Val d'Essonne and CNRS
*
* Postal address: LaMME, Bâtiment I.B.G.B.I., 3ème étage, 23 Bd. de France, 91037 Evry Cedex, France. Email address: christophe.profeta@univ-evry.fr
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Abstract

We show that under some slight assumptions, the positive sojourn time of a product of symmetric processes converges towards ½ as the number of processes increases. Monotony properties are then exhibited in the case of symmetric stable processes, and used, via a recurrence relation, to obtain upper and lower bounds on the moments of the occupation time (in the first and third quadrants) for two-dimensional Brownian motion. Explicit values are also given for the second and third moments in the n-dimensional Brownian case.

Keywords

Sojourn timearcsine lawstrong law of large numbers

MSC classification

Primary: 60F15: Strong theorems
Secondary: 60J65: Brownian motion 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 69 - 81
Copyright
Copyright © Applied Probability Trust 2018 

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