Introduction to Stochastic Analysis and Malliavin Calculus (Paperback, 2014)

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.