Ch. 1. Integration by parts and absolute continuity of probability laws -- ch. 2. Finite dimensional Malliavin calculus -- ch. 3. The basic operators of Malliavin calculus -- ch. 4. Representation of Wiener functionals -- ch. 5. Criteria for absolute continuity and smoothness of probability laws -- ch. 6. Stochastic partial differential equations driven by spatially homogeneous gaussian noise -- ch. 7. Malliavin regularity of solutions of SPDE's -- ch. 8. Analysis of the Malliavin matrix of solutions of SPDE's
Summary
Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics. This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself b
Bibliography
Includes bibliographical references (pages 155-160) and index
Notes
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