The Malliavin Calculus and Related Topics (Probability and Its Applications)

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Naor , Solution of Shannon's problem on the monotonicity of entropy , Journal of the American Mathematical Society , vol.

ISBN 13: 9783540283287

DOI : Carlen and D. Cattiaux and C. Leonard , Minimization of the Kullback information of diffusion processes , Annales de l'I. Driver , Towards calculus and geometry on path spaces , Proceedings of symposia in Pure Mathematics , Emery, S. Fang, and P. A , vol.

Introduction to Probability

Feyel and A. Feyel, A.

Additional information

XVII , Guerra and L. Morato , Quantization of dynamical systems and stochastic control theory, Physical review D , Gross , Logarithmic Sobolev inequalities, Amer , J.

Malliavin Calculus and Related Topics - PDF Free Download

Math , Kobayashi and K. Walsh Knowing the odds One should know the material in these books, end to end.

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  • The Malliavin Calculus and Related Topics | David Nualart | Springer.
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Many alternate books are possible, for example Probability: Theory and examples. For learning measure theory and probability, one could use Dudley's Analysis and probability while Grimmett and Stirzaker's Probability and random processes is good for pre-measure theoretical probability.

Also, solving problems from the above books or from this set , for example is recommended. Kallenberg's inimitable book Foundations of probability contains material worth other books, but my feeling is that it is best for the second reading rather than the first. Basic, but slightly more advanced Some of the topics that are basic but not adequately covered in the Durrett's book can be read from the following list.

This is a topic-wise listing, rather than a recommendation to read all the books cover to cover!

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Weak convergence theory from Billingsley's Weak convergence of probability measures or K. Parthasarathy's Probability measures on metric spaces. Stochastic Calculus Karatzas and Shreve Brownian motion and stochastic calculus Large deviations, at least Sanov's theorem Dembo and Zeitouni's Large deviations: techniques and applications and concentration of measure first three chapters of Boucheron, Lugosi and Massart's Concentration inequalities: a non-asymptotic theory of independence.

Discrete probability: The amazingly beautiful book Probability on trees and networks by Lyons and Peres, Grimmett's Probability on graphs and the superb lecture notes by Sebastain Roch and the well-known book The probabilistic method by Alon and Spencer.

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  6. More about Brownian motion, its connections to PDE etc. Varadhan's TIFR lecture notes Diffusions and partial differential equations Markov processes Liggett's Continuous time Markov processes: an introduction , just the first chapters would be good Mixing times of Markov chains book of the same name by Levin, Peres and Wilmer, a few chapters give sufficiently many of the ideas Gaussian Hilbert spaces Janson's Gaussian Hilbert spaces , initial part, is very good for learning Wiener chaos decomposition, Wick formula etc.

    Shreve , Brownian Motion and Stochastic Calculus. Springer-Verlag MR Zbl Malliavin , Stochastic calculus of variations and hypoelliptic operators , in Proc.

    Electronic Journal of Probability

    LNM Numdam Zbl Probability and its Applications. Springer-Verlag, 2nd Edition Nualart and M. Sanz , Malliavin calculus for two-parameter Wiener functionals. Gebiete 70 Protter , Stochastic Integration and Differential Equations.