Penalising Brownian Paths

Beschreibung

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.

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.

Autor*in

Bernard Roynette

Themen in »Penalising Brownian Paths«

Bessel process Brownian motion Martingale Martingales Penalisations Probability theory

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From the reviews: “In this book the authors give a systematic study of penalisation. The book is divided into 5 chapters. … This book is very useful for graduate students and researchers interested in learning penalisations.” (Ren Ming Song, Mathematical Reviews, Issue 2010 e)
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