دوره‌ای در حساب دیفرانسیل مالی، با کاربردهایی در PDEهای تصادفی جلد ۲

lecturenotes.pdf......Page 0 Introduction......Page 4 Integration by parts and absolute continuity of probability laws......Page 6 The Ornstein-Uhlenbeck operator......Page 10 The adjoint of the differential......Page 14 An integration by parts formula: Existence of density......Page 15 The Ornstein-Uhlenbeck operator......Page 18 The derivative operator......Page 21 The integral or divergence operator......Page 24 Differential Calculus......Page 25 Calculus with multiple Wiener integrals......Page 29 Local property of the operators......Page 33 The Itô integral and the divergence operator......Page 37 The Clark-Ocone formula......Page 39 Generalized Clark-Ocone formula......Page 40 Application to option pricing......Page 43 Existence of density......Page 49 Smoothness of the density......Page 52 Stochastic integration with respect to coloured noise......Page 55 Stochastic Partial Differential Equations driven by a coloured noise......Page 63 Malliavin regularity of solutions of SPDEs......Page 75 One dimensional case......Page 98 Examples......Page 109 Multidimensional case......Page 118 Definition of spaces used along the course......Page 123 References......Page 124