Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Stochastic processes --- 51 --- Mathematics --- 51 Mathematics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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 years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made.

Mathematics. --- Functional analysis. --- Measure theory. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Functional Analysis. --- Measure and Integration. --- Distribution (Probability theory. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Stochastic differential equations. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Reaction-diffusion equations --- Navier-Stokes equations --- Ergodic theory --- Stochastic analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Functional analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The aim of this book is to give a systematic and self-contained presentation of the basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by It and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measures on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof.

Stochastic partial differential equations --- Stochastic partial differential equations. --- Stochastic processes --- Équations aux dérivées partielles stochastiques