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Functional Integrals : Approximate Evaluations and Applications : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - A.D. Egorov

Functional Integrals : Approximate Evaluations and Applications

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover

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Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes. This monograph is devoted to numerical approximation methods of continual integration. A systematic description is given of the approximate computation methods of functional integrals on a wide class of measures, including measures generated by homogeneous random processes with independent increments and Gaussian processes. Many applications to problems which originate from analysis, probability and quantum physics are presented. This book will be of interest to mathematicians and physicists, including specialists in computational mathematics, functional and statistical physics, nuclear physics and quantum optics.

Preface
Backgrounds from Analysis on Linear Topological Spacesp. 1
Integrals with Respect to Gaussian Measures and Some Quasimeasures: Exact Formulae, Wick Polynomials, Diagramsp. 15
Integration in Linear Topological Spaces of Some Special Classesp. 47
Approximate Interpolation-Type Formulaep. 65
Formulae Based on Characteristic Functional Approximations, which Preserve a Given Number of Momentsp. 81
Integrals with Respect to Gaussian Measuresp. 109
Integrals with Respect to Conditional Wiener Measurep. 147
Integrals with Respect to Measures which Correspond to Uniform Processes with Independent Incrementsp. 167
Approximations which Agree with Diagram Approachesp. 211
Approximations of Integrals Based on Interpolation of Measurep. 235
Integrals with Respect to Measures Generated by Solutions of Stochastic Equations. Integrals Over Manifoldsp. 249
Quadrature Formulae for Integrals of Special Formp. 277
Evaluation of Integrals by Monte-Carlo Methodp. 327
Approximate Formulae for Multiple Integrals with Respect to Gaussian Measurep. 343
Some Special Problems of Functional Integrationp. 367
Bibliographyp. 401
Indexp. 417
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792321934
ISBN-10: 0792321936
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 419
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 17.15  x 2.54
Weight (kg): 0.91