Roynette B., Yor M. Penalising Brownian paths 2009

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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.
Front Matter
Introduction
Some penalisations of the Wiener measure
Feynman-Kac penalisations for Brownian motion
Penalisations of a Bessel process with dimension d(0 d 2) by a function of the ranked lengths of its excursions
A general principle and some questions about penalisations
Back Matter