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Some penalisations of the Wiener measure

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Japan. J. Math. 1, 263–290 (2006) DOI: 10.1007/s11537-006-0507-0

Some penalisations of the Wiener measure

B. Roynette · P. Vallois · M. Yor

Received: 29 November 2005 / Accepted: 10 February 2006 Published online: 2 April 2006

c The Mathematical Society of Japan and Springer-Verlag 2006 Communicated by: Toshiyuki Kobayashi

Abstract. A number of limit laws, which are obtained from various penalisations of the Wiener measure on C(R+,Rd), are shown to exist, and are described thoroughly, with the help of path decompositions.

Keywords and phrases: Brownian motion, Wiener measure, 3-dimensional Bessel process, path decompositions, supremum process, L´evy and Pitman theorems, age process of excursions, Brow- nian windings

Mathematics Subject Classification (2000): 60F17, 60F99, 60G44, 60H20, 60J60

B. ROYNETTE

Universit´e Henri Poincar´e, Institut Elie Cartan, BP239, F-54506 Vandoeuvre-les-Nancy Cedex, France

P. VALLOIS

Universit´e Henri Poincar´e, Institut Elie Cartan, BP239, F-54506 Vandoeuvre-les-Nancy Cedex, France

M. YOR

Laboratoire de Probabilit´es et Mod`eles Al´eatoires, Universit´es Paris VI et VII, 4 Place Jussieu- Case 188, F-75252 Paris Cedex 05, France and Institut Universitaire de France

(e-mail:[email protected])

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