Penalising Brownian Paths [electronic resource] / by Bernard Roynette, Marc Yor.
Material type: TextSeries: Lecture Notes in Mathematics ; 1969Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: XIII, 275 p. online resourceContent type:- text
- computer
- online resource
- 9783540896999
- 519.2 23
- QA273.A1-274.9
- QA274-274.9
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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