Introduction to Stochastic Analysis and Malliavin Calculus

This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Da Prato, Giuseppe (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2014.
Edición:1st ed. 2014.
Colección:Lecture Notes (Scuola Normale Superiore), 13
Temas:
Probabilities.
Functional analysis.
Measure theory.
Probability Theory.
Functional Analysis.
Measure and Integration.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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