Pinning class of the Wiener measure by a functional: related martingales and invariance properties |
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| Authors: | Fabrice?Baudoin Email author" target="_blank">Michèle?ThieullenEmail author |
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| Institution: | (1) Department of Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/105, 1040 Vienna, Austria;(2) Laboratoire de Probabilités et Modèles aléatoires, Université Paris 6, Boîte 188, 4 Place Jussieu, 75252 Paris Cédex 05, France |
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| Abstract: | For a given functional Y on the path space, we define the pinning class of the Wiener measure as the class of probabilities which admit the same conditioning given Y as the Wiener measure. Using stochastic analysis and the theory of initial enlargement of filtration, we study the transformations (not necessarily adapted) which preserve this class. We prove, in this non Markov setting, a stochastic Newton equation and a stochastic Noether theorem. We conclude the paper with some non canonical representations of Brownian motion, closely related to our study.Mathematics Subject Classification (2000): 60G44, 60H07, 60H20, 60H30 |
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| Keywords: | Conditioned stochastic differential equation Initial enlargement of filtrations Newton martingale Noether stochastic theorem Stochastic analysis Symmetries in stochastic calculus |
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