Penalising Brownian Paths [electronic resource] / by Bernard Roynette, Marc Yor.
Tipo de material:
TextoSeries Lecture Notes in Mathematics, 1969Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Descripción: online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783540896999Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic ProcessesFormatos físicos adicionales: Sin títuloRecursos en línea: de clik aquí para ver el libro electrónico 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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