Penalising Brownian Paths
Roynette, Bernard.
Penalising Brownian Paths [electronic resource] / by Bernard Roynette, Marc Yor. - XIII, 275 p. online resource. - Lecture Notes in Mathematics, 1969 0075-8434 ; . - Lecture Notes in Mathematics, 1969 .
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.
9783540896999
10.1007/978-3-540-89699-9 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2
Penalising Brownian Paths [electronic resource] / by Bernard Roynette, Marc Yor. - XIII, 275 p. online resource. - Lecture Notes in Mathematics, 1969 0075-8434 ; . - Lecture Notes in Mathematics, 1969 .
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.
9783540896999
10.1007/978-3-540-89699-9 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2