Functional Integrals

1. Front Matter

   Pages i-x

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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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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.

• Approximation
• Gaussian measure
• Gaussian process
• Integral equation
• Interpolation
• Probability theory
• STATISTICA

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

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

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