Brownian processes in infinite dimension |
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| Authors: | Denis Feyel Arnaud de la Pradelle |
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| Institution: | (1) Equipe d'Analyse et de Probabilités, Université d'Evry-Val d'Essonne, Bureau 336, Boulevard des Coquibus, 91025 Evry Cedex, France;(2) Université Paris VI, UA 754 au CNRS, Tour 46-0, bureau 413, 4 place Jussieu, 75230 Paris Cedex 05, France |
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| Abstract: | LetE be a locally convex space endowed with a centered gaussian measure  . We construct a continuousE-valued brownian motionW
t with covariance . The main goal is to solve the SDE of Langevin type dX
t=
dW
t–AX
t wherea andA are unbounded operators of the Cameron-Martin space of (E, ). It appears as the unique linear measurable extension of the solution of the classical Cauchy problemv (t)=
u–Av(t). |
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| Keywords: | 34F05 60G15 60H10 60J65 |
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