Degenerate Stochastic Differential Equations and Hypoellipticity: 1st Edition (Hardback) book cover

Degenerate Stochastic Differential Equations and Hypoellipticity

1st Edition

By Denis Bell

Chapman and Hall/CRC

128 pages

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Hardback: 9780582246898
pub: 1996-05-15
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The main theme of this Monograph is the study of degenerate stochastic differential equations, considered as transformations of the Wiener measure, and their relationship with partial differential equations. The book contains an elementary derivation of Malliavin's integration by parts formula, a proof of the probabilistic form of Hormander's theorem, an extension of Hormander's theorem for infinitely degenerate differential operators, and criteria for the regularity of measures induced by stochastic

hereditary-delay equations.


"This monograph is an excellent and well written text on the

applications of Malliavin calculus, and it can be very helpful to

researchers interested in these subjects."

-Zentralblatt fur Mathematik 859

Table of Contents


List of notations


1. Background material

2. Regularity of measures induced by stochastic differential equations

3. The probabilistic form of Hormander's theorem

4. Infinitely degenerate hypoelliptic operators

5. Smooth densities for a class of stochastic functional equations

6. Generalized divergence operators and absolutely continuous transformations


About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations