Penalising Brownian Paths

Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theor...

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Bibliographic Details
Main Authors: Roynette, Bernard. (Author), Yor, Marc. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
Series:Lecture Notes in Mathematics, 1969
Subjects:
Online Access:https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-89699-9
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505 0 # |a Introduction -- 1 Some Penalisations of Wiener Measure -- 2 Feynman-Kac Penalisations for Brownian Motion -- 3 Penalisations of a Bessel Process with Dimension d (0<d<2) by a Function of the Ranked Lengths of its Excursions -- 4 A General Principle and some Questions About Penalisations. 
520 # # |a Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account. 
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