Brownian motion -- Stochastic calculus -- Derivative and divergence operators -- Wiener chaos -- Ornstein-Uhlenbeck semigroup -- Stochastic integral representations -- Study of densities -- Normal approximations -- Jump processes -- Malliavin calculus for jump processes I -- Malliavin calculus for jump processes II.
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This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.