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Penalising Brownian Paths [electronic resource] /by Bernard Roynette, Marc Yor.

by Roynette, Bernard [author.]; Yor, Marc [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 1969Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.Description: online resource.ISBN: 9783540896999.Subject(s): Mathematics | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic ProcessesOnline resources: Click here to access online
Contents:
Some penalisations of theWiener 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.
In: Springer eBooksSummary: 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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Some penalisations of theWiener 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.

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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