Functional integrals: approximate evaluation and applications
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Series: | Mathematics and its applications
249 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | X, 418 S. |
| ISBN: | 0792321936 |
Staff View
MARC
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| 100 | 1 | |a Egorov, Aleksandr D. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Približennye metody vyčislenija kontinual'nych integralov |
| 245 | 1 | 0 | |a Functional integrals |b approximate evaluation and applications |c by A. D. Egorov, P. I. Sobolevsky and L. A. Yanovich |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
| 300 | |a X, 418 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 249 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 7 | |a Espaces vectoriels topologiques |2 ram | |
| 650 | 7 | |a Intégration de fonctions |2 ram | |
| 650 | 4 | |a Integration, Functional | |
| 650 | 4 | |a Linear topological spaces | |
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| 700 | 1 | |a Sobolevskij, Pavel I. |e Verfasser |4 aut | |
| 700 | 1 | |a Janovič, Leonid A. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
1 Backgrounds from Analysis on Linear Topological Spaces 1
1.1 Cylindric Functions, Functional Polynomials, Derivatives 1
1.2 Definition of Functional Integrals with Respect to Measure, Quasi
measure and Pseudomeasure, Relations with Random Process
Theory 5
1.3 Characteristic Functionals of Measures 7
1.4 Moments, Semi invariants, Integrals of Cylindric Functions 11
2 Integrals with Respect to Gaussian Measures and Some
Quasimeasures: Exact Formulae, Wick Polynomials, Diagrams 15
2.1 Some Properties of Spaces with Gaussian Measure. Formulae
for Change of Integration Variables 15
2.2 Exact Formulae for Integrals of Special Functionals. Infinitesimal
Change of Measure 20
2.3 Integrals of Variations and of Derivatives of Functionals. Wick
Ordering. Diagrams 26
2.4 Integration with Respect to Gaussian Measure in Particular Spaces 34
3 Integration in Linear Topological Spaces of Some Special Classes 47
3.1 Inductive Limits of Linear Topological Spaces 47
3.2 Projective Limits of Linear Topological Spaces 48
3.3 Generalized Function Spaces 52
3.4 Integrals in Product Spaces 55
4 Approximate Interpolation Type Formulae 65
4.1 Interpolation of Functionals 65
4.2 Repeated Interpolation. Taylor s Formula 67
4.3 Construction Rules for Divided Difference Operators 68
4.4 Approximate Interpolation Formulae 77
5 Formulae Based on Characteristic Functional Approximations,
which Preserve a Given Number of Moments 81
5.1 Approximations of Characteristic Functionals 81
5.2 Reducing the Number of Terms in Approximations 89
5.3 Approximate Formulae 101
6 Integrals with Respect to Gaussian Measures 109
6.1 Formulae of Given Accuracy in Linear Topological Spaces 109
6.2 Formulae Based on Approximations of the Correlation Functional 119
vi
6.3 Stationary Gaussian Measures 128
6.4 Error Estimates for Approximate Formulae Based on Approxi¬
mations of the Argument 130
6.5 Formulae which are Exact for Special Kinds of Functionals 134
6.6 Convergence of Functional Quadrature Processes 139
7 Integrals with Respect to Conditional Wiener Measure 147
7.1 Approximations of Conditional Wiener Process which Preserve a
Given Number of Moments 147
7.2 Formulae of First Accuracy Degree 155
7.3 Third Accuracy Degree 158
7.4 Arbitrary Accuracy Degree 161
8 Integrals with Respect to Measures which Correspond to
Uniform Processes with Independent Increments 167
8.1 Formulae of First, Third and Fifth Accuracy Degrees 168
8.2 Arbitrary Accuracy Degree 176
8.3 Integrals with Respect to Measures Generated by Multidimen¬
sional Processes 189
8.4 Convergence of Composite Formulae 193
8.5 Cubature Formulae for Multiple Probabilistic Integrals 200
9 Approximations which Agree with Diagram Approaches 211
9.1 Formulae which are Exact for Polynomials of Wick Powers 211
9.2 Approximate Integration of Functionals of Wick Exponents 215
9.3 Formulae which are Exact for Diagrams of a Given Type 219
9.4 Approximate Formulae for Integrals with Respect to Quasimeasures 226
9.5 Some Extensions. Composite Formulae 229
10 Approximations of Integrals Based on Interpolation of Measure 235
10.1 Approximations of Integrals with Respect to Ornstein Uhlenbeck
Measure 235
10.2 Integrals with Respect to Wiener Measure, Conditional Wiener
Measure, and Modular Measure 241
10.3 Formulae Based on Measure Interpolation for Integrals of
Non Differentiate Functionals 245
11 Integrals with Respect to Measures Generated by Solutions of
Stochastic Equations. Integrals Over Manifolds 249
11.1 Approximate Formulae for Integrals with Respect to Measures
Generated by Solutions of Stochastic Equations 249
11.2 Approximations of Integrals with Respect to Measures Generated
by Stochastic Differential Equations over Martingales 253
vii
11.3 Formula of Infinitesimal Change of Measure in Integrals with
Respect to Measures Generated by Solutions of Ito Equations 260
11.4 Approximate Formulae for Integrals over Manifolds 266
12 Quadrature Formulae for Integrals of Special Form 277
12.1 Formulae Based on Algebraic Interpolation 277
12.2 Formulae Based on Trigonometric Interpolation 282
12.3 Quadrature Formulae with Equal Coefficients 292
12.4 Tables of Nodes and Coefficients of Quadrature Formula of Highest
Accuracy Degree for Some Integrals 300
12.5 Formulae with the Minimal Residual Estimate 319
13 Evaluation of Integrals by Monte Carlo Method 327
13.1 Definitions and Facts Related to Monte Carlo Method 327
13.2 Estimates for Integrals with Respect to Wiener Measure 331
13.3 Estimation of Integrals with Respect to Arbitrary Gaussian Measure
in Space of Continuous Functions 334
13.4 A Sharper Monte Carlo Estimate of Functional Integrals 338
14 Approximate Formulae for Multiple Integrals with Respect to
Gaussian Measure 343
14.1 Formulae of Third Accuracy Degree 344
14.2 Formulae of Fifth Accuracy Degree 350
14.3 Formulae of Seventh Accuracy Degree 357
14.4 Cubature Formulae for Multiple Integrals of a Certain Kind 359
15 Some Special Problems of Functional Integration 367
15.1 Application of Functional Integrals to Solution of Certain Kinds
of Equations 367
15.2 Application of Approximations Based on Measure Interpolation
to Evaluation of Ground State Energy for Certain Quantum
Systems 375
15.3 Mean Square Approximation of Some Classes of Linear Functionals 378
15.4 Exact Formulae for Integrals with Respect to Gaussian and
Conditional Gaussian Measures of Special Types of Functionals 391
Bibliography 401
Index 417
|
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| author | Egorov, Aleksandr D. Sobolevskij, Pavel I. Janovič, Leonid A. |
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| discipline | Mathematik |
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| id | DE-604.BV007662705 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:07:10Z |
| institution | BVB |
| isbn | 0792321936 |
| language | English Russian |
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| physical | X, 418 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Egorov, Aleksandr D. Verfasser aut Približennye metody vyčislenija kontinual'nych integralov Functional integrals approximate evaluation and applications by A. D. Egorov, P. I. Sobolevsky and L. A. Yanovich Dordrecht u.a. Kluwer Acad. Publ. 1993 X, 418 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 249 Aus d. Russ. übers. Espaces vectoriels topologiques ram Intégration de fonctions ram Integration, Functional Linear topological spaces Funktionalintegration (DE-588)4155674-4 gnd rswk-swf Funktionalintegration (DE-588)4155674-4 s DE-604 Sobolevskij, Pavel I. Verfasser aut Janovič, Leonid A. Verfasser aut Mathematics and its applications 249 (DE-604)BV008163334 249 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005024572&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Egorov, Aleksandr D. Sobolevskij, Pavel I. Janovič, Leonid A. Functional integrals approximate evaluation and applications Mathematics and its applications Espaces vectoriels topologiques ram Intégration de fonctions ram Integration, Functional Linear topological spaces Funktionalintegration (DE-588)4155674-4 gnd |
| subject_GND | (DE-588)4155674-4 |
| title | Functional integrals approximate evaluation and applications |
| title_alt | Približennye metody vyčislenija kontinual'nych integralov |
| title_auth | Functional integrals approximate evaluation and applications |
| title_exact_search | Functional integrals approximate evaluation and applications |
| title_full | Functional integrals approximate evaluation and applications by A. D. Egorov, P. I. Sobolevsky and L. A. Yanovich |
| title_fullStr | Functional integrals approximate evaluation and applications by A. D. Egorov, P. I. Sobolevsky and L. A. Yanovich |
| title_full_unstemmed | Functional integrals approximate evaluation and applications by A. D. Egorov, P. I. Sobolevsky and L. A. Yanovich |
| title_short | Functional integrals |
| title_sort | functional integrals approximate evaluation and applications |
| title_sub | approximate evaluation and applications |
| topic | Espaces vectoriels topologiques ram Intégration de fonctions ram Integration, Functional Linear topological spaces Funktionalintegration (DE-588)4155674-4 gnd |
| topic_facet | Espaces vectoriels topologiques Intégration de fonctions Integration, Functional Linear topological spaces Funktionalintegration |
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