TY - GEN AU - Prato,Giuseppe Da TI - Introduction to stochastic analysis and Malliavin calculus SN - 9788876424977 U1 - 519.23 23 PY - 2014/// CY - Pisa : PB - Edizioni Della Normale KW - Stochastic differential equations. KW - Malliavin calculus KW - Stochastische analyse N1 - Includes bibliographical references; Introduction.- 1 Gaussian measures in Hilbert spaces.- 2 Gaussian random variables.- 3 The Malliavin derivative.- 4 Brownian Motion.- 5 Markov property of Brownian motion.- 6 Ito's integral.- 7 Ito's formula.- 8 Stochastic differential equations.- 9 Relationship between stochastic and parabolic equations.- 10 Formulae of Feynman-Kac and Girsanov.- 11 Malliavin calculus.- 12 Asymptotic behaviour of transition semigroups.- A The Dynkin Theorem.- B Conditional expectation.- C Martingales.- D Fixed points depending on parameters.- E A basic ergodic theorem.- References N2 - This book introduces differential stochastic equations and Malliavin calculus. The revised and expanded third edition offers corrections and improvements and a new section covering the differentiability of the Feynman-Kac semigroup ER -