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An introduction to Malliavin calculus and some of its applications. (English) Zbl 0729.60046
Recent advances in stochastic calculus, Mater. Lect. Ser., College Park/MD (USA) 1987, Prog. Autom. Inf. Syst., 65-104 (1990).
[For the entire collection see Zbl 0701.00026.]
By a set of notes on Malliavin calculus (the cases of a finite- dimensional probability space, the basic definitions and results on Wiener space, applications to the solution of Stratonovich differential equation and nonlinear filtering problems, Skorokhod integrals and generalized Itô’s and Stratonovich’s formulas) the authors succeeded in introducing and reflecting the study of the theory until 1986 [see e.g., D. Nualart and the second author, Probab. Theory Relat. Fields 78, No.4, 535-581 (1988; Zbl 0629.60061)]. An extended bibliography for the two last notes is included at the end. No detailed proof is given and each section is followed by bibliographical comments. Some of the relevant techniques together with a classical example of a hypoelliptic diffusion are presented.
Reviewer: T.N.Pham (Hanoi)

MSC:
60H07 Stochastic calculus of variations and the Malliavin calculus
60H05 Stochastic integrals