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Functional Integrals

Approximate Evaluation and Applications

  • Book
  • © 1993

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Authors:
  1. A. D. Egorov

    1. Institute of Mathematics, Belarus Academy of Sciences, Minsk, Byelo-Russia

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  2. P. I. Sobolevsky

    1. Institute of Mathematics, Belarus Academy of Sciences, Minsk, Byelo-Russia

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    You can also search for this author in PubMed   Google Scholar

  3. L. A. Yanovich

    1. Institute of Mathematics, Belarus Academy of Sciences, Minsk, Byelo-Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 249)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Backgrounds from Analysis on Linear Topological Spaces

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 1-14

  3. Integrals with Respect to Gaussian Measures and Some Quasimeasures: Exact Formulae, Wick Polynomials, Diagrams

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 15-46

  4. Integration in Linear Topological Spaces of Some Special Classes

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 47-63

  5. Approximate Interpolation-Type Formulae

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 65-80

  6. Formulae Based on Characteristic Functional Approximations, which Preserve a Given Number of Moments

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 81-107

  7. Integrals with Respect to Gaussian Measures

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 109-146

  8. Integrals with Respect to Conditional Wiener Measure

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 147-165

  9. Integrals With Respect to Measures which Correspond to Uniform Processes with Independent Increments

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 167-209

  10. Approximations which Agree with Diagram Approaches

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 211-233

  11. Approximations of Integrals Based on Interpolation of Measure

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 235-248

  12. Integrals with Respect to Measures Generated by Solutions of Stochastic Equations. Integrals Over Manifolds

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 249-276

  13. Quadrature Formulae for Integrals of Special Form

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 277-325

  14. Evaluation of Integrals by Monte-Carlo Method

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 327-342

  15. Approximate Formulae for Multiple Integrals with Respect to Gaussian Measure

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 343-365

  16. Some Special Problems of Functional Integration

    • A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich
    Pages 367-400

  17. Back Matter

    Pages 401-419
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Keywords

About this book

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.

Authors and Affiliations

  • Institute of Mathematics, Belarus Academy of Sciences, Minsk, Byelo-Russia

    A. D. Egorov, P. I. Sobolevsky, L. A. Yanovich

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