Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / N.U. Ahmed.

Format:

Book

Author/Creator:

Ahmed, N. U. (Nasir Uddin)

Language:

English

Subjects (All):

Brownian motion processes.

Stochastic processes.

Physical Description:

1 online resource (314 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack : World Scientific, c2012.

Language Note:

English

Summary:

This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develop

Contents:

Preface; Contents; 1. Background Material; 1.1 Introduction; 1.2 Wiener Process and Wiener Measure; 1.3 Stochastic Differential Equations in Rd; 1.4 Stochastic Differential Equations in H; 1.4.1 Measure Solutions; 1.5 Nonlinear Filtering; 1.5.1 Finite Dimensional Filtering; 1.5.2 Infinite Dimensional Filtering; 1.6 Elements of Vector Measures; 1.7 Some Problems for Exercise; 2. Regular Functionals of Brownian Motion; 2.1 Introduction; 2.2 Functionals of Scalar Brownian Motion; 2.3 Functionals of Vector Brownian Motion; 2.4 Functionals of Gaussian Random Field (GRF)

5.6 Some Problems for Exercise6. Lp-Based Generalized Functionals of White Noise III; 6.1 Introduction; 6.2 Homogeneous Functionals of Degree n; 6.3 Nonhomogeneous Functionals; 6.4 Weighted Generalized Functionals; 6.5 Some Examples Related to Section 6.4; 6.6 Generalized Functionals of Random Fields Applied; 6.7 ̃ Fq-Valued Vector Measures with Application; 6.8 Some Problems for Exercise; 7. Wp,m-Based Generalized Functionals of White Noise IV; 7.1 Introduction; 7.2 Homogeneous Functionals; 7.3 Nonhomogeneous Functionals; 7.4 Inductive and Projective Limits

8.7.2 Smoothness under H ̈ormander's Conditions

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 291-296) and index.

ISBN:

9786613555441

9781280377532

1280377534

9789814366373

9814366374

OCLC:

877767936