Penalising Brownian Paths [electronic resource] / by Bernard Roynette, Marc Yor.
Material type: TextSeries: Lecture Notes in Mathematics ; 1969Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540896999Subject(s): Mathematics | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic ProcessesAdditional physical formats: Printed edition:: No titleOnline resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1910 |
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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