Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Brownian penalisations related to excursion lengths, VII

B. Roynette, P. Vallois, and M. Yor

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Abstract

Limiting laws, as t→∞, for Brownian motion penalised by the longest length of excursions up to t, or up to the last zero before t, or again, up to the first zero after t, are shown to exist, and are characterized.

Résumé

Il est prouvé que les lois limites, lorsque t→∞, du mouvement brownien pénalisé par la plus grande longueur des excursions jusqu’en t, ou bien jusqu’au dernier zéro avant t, ou encore jusqu’au premier zéro après t, existent. Ces lois limites sont décrites en détail.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 45, Number 2 (2009), 421-452.

Dates
First available in Project Euclid: 29 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1241024675

Digital Object Identifier
doi:10.1214/08-AIHP177

Mathematical Reviews number (MathSciNet)
MR2521408

Zentralblatt MATH identifier
1181.60046

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60F99: None of the above, but in this section 60G17: Sample path properties 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G44: Martingales with continuous parameter 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations 60J25: Continuous-time Markov processes on general state spaces 60J55: Local time and additive functionals 60J60: Diffusion processes [See also 58J65] 60J65: Brownian motion [See also 58J65]

Keywords
Longest length of excursions Brownian meander Penalisation

Citation

Roynette, B.; Vallois, P.; Yor, M. Brownian penalisations related to excursion lengths, VII. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), no. 2, 421--452. doi:10.1214/08-AIHP177. https://projecteuclid.org/euclid.aihp/1241024675


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