Stochastic equations in infinite dimensions [E-Book] / Giuseppe Da Prato, Scuola Normale Superiore, Pisa, Jerzy Zabczyk, Polish Academy of Sciences.
Da Prato, Giuseppe, (author)
Zabczyk, Jerzy, (author)
Second edition.
Cambridge : Cambridge University Press, 2014
1 online resource (xviii, 493 pages)
Encyclopedia of mathematics and its applications ; volume 152
Full Text
Table of Contents:
  • Introduction: motivating examples
  • Part One: Foundations
  • Random variables
  • Probability measures
  • Stochastic processes
  • The stochastic integral
  • Part Two: Existence and uniqueness
  • Linear equations with additive noise
  • Linear equations with multiplicative noise
  • Existence and uniqueness for nonlinear equations
  • Martingale solutions
  • Part Three: Properties of solutions
  • Markov property and Kolmogorov equation
  • Absolute continuity and the Girsanov theorem
  • Large time behavior of solutions
  • Small noise asymptotic behavior
  • Survey of specific equations
  • Some recent developments.