Researches in Stochastic Analysis
 — Arnaud de La Pradelle & Denis Feyel

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ISBN : 978-2-36693-026-9
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Fundamentally this book presents an analytic point of view on the probability theory of processes and emphasizes the strong connections between classical Potential Theory and Brownian motion. Since well-known superharmonic functions and supermartingales are so closely related that the filtering theory of processes can be seen as a particular Potential theory, they are analyzed here by the use of a common framework. This framework is the space L1(c) where c is a capacity, that is, roughly speaking, a sublinear functional, as first considered by B. Fuglede.

An associated notion of quasi-topology is defined that gives a very good account of the classical quasi- continuous functions in the finite or the infinite dimensional case of the Malliavin calculus on a Wiener space.

Denis Feyel

Laboratory of Mathématiques et Modélisation, Evry Val d'Essonne University, France.

Doistau-Blutel prize from the French Science Academy (1982).

Special invitation to French Professor at Wuhan university, China (1983-1985).

Editor-in-chief and founder of the journal Potential Analysis.

Arnaud de la Pradelle

Analysis team, C.N.R.S. n°294, Paris VI University, France.

Secretary general of the Laplace-Gauss association whose aim is to support collective initiative in the field of Stochastic Analysis.

They were both former pupils of Marcel Brelot and active members of the Brelot-Choquet-Deny seminar in Potential theory.

title = {Researches in Stochastic Analysis},
author = {de La Pradelle, Arnaud and Feyel, Denis},
year = {2017},
publisher = {Spartacus-Idh},
ISBN = {978-2-36693-026-9},
pages = {158},
url = {}

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