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catalog alternative "Gaussovskie mery. English".
catalog contributor b10956726.
catalog created "c1998.".
catalog date "1998".
catalog date "c1998.".
catalog dateCopyrighted "c1998.".
catalog description "187 -- 4.9. Large deviations 195 -- 4.10. Complements and problems 197 -- Chapter 5. Sobolev Classes over Gaussian Measures 205 -- 5.1. Integration by parts 205 -- 5.2. The Sobolev classes W[superscript p, r] and D[superscript p, n] 211 -- 5.3. The Sobolev classes H[superscript p, r] 215 -- 5.4. Properties of Sobolev classes and examples 218 -- 5.5. The logarithmic Sobolev inequality 226 -- 5.6. Multipliers and Meyer's inequalities 229 -- 5.7. Equivalence of different definitions 234 -- 5.8. Divergence of vector fields 238 -- 5.9. Gaussian capacities 243 -- 5.10. Measurable polynomials 249 -- 5.11. Differentiability of H-Lipschitzian functions 261 -- 5.12. Complements and problems 266 -- Chapter 6. Nonlinear Transofrmations of Gaussian Measures 279 -- 6.1. Auxiliary results 279 -- 6.2. Measurable linear automorphisms 282 -- 6.3. Linear transformations 285 -- 6.4.".
catalog description "Chapter 1. Finite Dimensional Gaussian Distributions 1 -- 1.1. Gaussian measures on the real line 1 -- 1.2. Multivariate Gaussian distributions 3 -- 1.3. Hermite polynomials 7 -- 1.4. The Ornstein-Uhlenbeck semigroup 9 -- 1.5. Sobolev classes 12 -- 1.6. Hypercontractivity 16 -- 1.7. Several useful estimates 19 -- 1.8. Convexity inequalities 25 -- 1.9. Characterizations of Gaussian measures 30 -- 1.10. Complements and problems 33 -- Chapter 2. Infinite Dimensional Gaussian Distributions 39 -- 2.1. Cylindrical sets 39 -- 2.2. Basic definitions 42 -- 2.4. The Cameron-Martin space 59 -- 2.5. Zero-one laws 64 -- 2.6. Separability and oscillations 67 -- 2.7. Equivalence and singularity 71 -- 2.8. Measurable seminorms 74 -- 2.9. The Ornstein-Uhlenbeck semigroup 78 -- 2.10. Measurable linear functionals 79 -- 2.11. Stochastic integrals 83 -- 2.12.".
catalog description "Complements and problems 90 -- Chapter 3. Radon Gaussian Measures 97 -- 3.1. Radon measures 97 -- 3.2. Basic properties of Radon Gaussian measures 100 -- 3.3. Gaussian covariances 104 -- 3.4. The structure of Radon Gaussian measures 109 -- 3.5. Gaussian series 112 -- 3.6. Supports of Gaussian measures 119 -- 3.7. Measurable linear operators 122 -- 3.8. Weak convergence of Gaussian measures 129 -- 3.9. Abstract Wiener spaces 136 -- 3.10. Conditional measures and conditional expectations 140 -- 3.11. Complements and problems 142 -- Chapter 4. Convexity of Gaussian Measures 157 -- 4.1. Gaussian symmetrization 157 -- 4.2. Ehrhard's inequality 162 -- 4.3. Isoperimetric inequalities 167 -- 4.4. Convex functions 171 -- 4.5. H-Lipschitzian functions 174 -- 4.6. Correlation inequalities 177 -- 4.7. The Onsager-Machlup functions 181 -- 4.8. Small ball probabilities".
catalog description "Includes bibliographical references (p. 391-426) and index.".
catalog description "Radon-Nikodym densities 288 -- 6.5. Examples of equivalent measures and linear transformations 295 -- 6.6. Nonlinear transformations 298 -- 6.7. Examples of nonlinear transformations 308 -- 6.8. Finite dimensional mappings 314 -- 6.9. Malliavin's method 316 -- 6.10. Surface measures 321 -- 6.11. Complements and problems 324 -- Chapter 7. Applications 333 -- 7.1. Trajectories of Gaussian processes 333 -- 7.2. Infinite dimensional Wiener processes 336 -- 7.3. Logarithmic gradients 339 -- 7.4. Spherically symmetric measures 344 -- 7.5. Infinite dimensional diffusions 346 -- 7.6. Complements and problems 353 -- Appendix A. Locally Convex Spaces, Operators, and Measures 361 -- A.1. Locally convex spaces 361 -- A.2. Linear operators 365 -- A.3. Measures and measurability 371.".
catalog extent "xii, 433 p. ;".
catalog identifier "0821810545 (hc : alk. paper)".
catalog isPartOf "Mathematical surveys and monographs ; no. 62.".
catalog isPartOf "Mathematical surveys and monographs, 0076-5376 ; v. 62".
catalog issued "1998".
catalog issued "c1998.".
catalog language "eng rus".
catalog language "eng".
catalog publisher "Providence, R.I. : American Mathematical Society,".
catalog subject "515/.42 21".
catalog subject "Gaussian measures.".
catalog subject "QA312 .B6413 1998".
catalog tableOfContents "187 -- 4.9. Large deviations 195 -- 4.10. Complements and problems 197 -- Chapter 5. Sobolev Classes over Gaussian Measures 205 -- 5.1. Integration by parts 205 -- 5.2. The Sobolev classes W[superscript p, r] and D[superscript p, n] 211 -- 5.3. The Sobolev classes H[superscript p, r] 215 -- 5.4. Properties of Sobolev classes and examples 218 -- 5.5. The logarithmic Sobolev inequality 226 -- 5.6. Multipliers and Meyer's inequalities 229 -- 5.7. Equivalence of different definitions 234 -- 5.8. Divergence of vector fields 238 -- 5.9. Gaussian capacities 243 -- 5.10. Measurable polynomials 249 -- 5.11. Differentiability of H-Lipschitzian functions 261 -- 5.12. Complements and problems 266 -- Chapter 6. Nonlinear Transofrmations of Gaussian Measures 279 -- 6.1. Auxiliary results 279 -- 6.2. Measurable linear automorphisms 282 -- 6.3. Linear transformations 285 -- 6.4.".
catalog tableOfContents "Chapter 1. Finite Dimensional Gaussian Distributions 1 -- 1.1. Gaussian measures on the real line 1 -- 1.2. Multivariate Gaussian distributions 3 -- 1.3. Hermite polynomials 7 -- 1.4. The Ornstein-Uhlenbeck semigroup 9 -- 1.5. Sobolev classes 12 -- 1.6. Hypercontractivity 16 -- 1.7. Several useful estimates 19 -- 1.8. Convexity inequalities 25 -- 1.9. Characterizations of Gaussian measures 30 -- 1.10. Complements and problems 33 -- Chapter 2. Infinite Dimensional Gaussian Distributions 39 -- 2.1. Cylindrical sets 39 -- 2.2. Basic definitions 42 -- 2.4. The Cameron-Martin space 59 -- 2.5. Zero-one laws 64 -- 2.6. Separability and oscillations 67 -- 2.7. Equivalence and singularity 71 -- 2.8. Measurable seminorms 74 -- 2.9. The Ornstein-Uhlenbeck semigroup 78 -- 2.10. Measurable linear functionals 79 -- 2.11. Stochastic integrals 83 -- 2.12.".
catalog tableOfContents "Complements and problems 90 -- Chapter 3. Radon Gaussian Measures 97 -- 3.1. Radon measures 97 -- 3.2. Basic properties of Radon Gaussian measures 100 -- 3.3. Gaussian covariances 104 -- 3.4. The structure of Radon Gaussian measures 109 -- 3.5. Gaussian series 112 -- 3.6. Supports of Gaussian measures 119 -- 3.7. Measurable linear operators 122 -- 3.8. Weak convergence of Gaussian measures 129 -- 3.9. Abstract Wiener spaces 136 -- 3.10. Conditional measures and conditional expectations 140 -- 3.11. Complements and problems 142 -- Chapter 4. Convexity of Gaussian Measures 157 -- 4.1. Gaussian symmetrization 157 -- 4.2. Ehrhard's inequality 162 -- 4.3. Isoperimetric inequalities 167 -- 4.4. Convex functions 171 -- 4.5. H-Lipschitzian functions 174 -- 4.6. Correlation inequalities 177 -- 4.7. The Onsager-Machlup functions 181 -- 4.8. Small ball probabilities".
catalog tableOfContents "Radon-Nikodym densities 288 -- 6.5. Examples of equivalent measures and linear transformations 295 -- 6.6. Nonlinear transformations 298 -- 6.7. Examples of nonlinear transformations 308 -- 6.8. Finite dimensional mappings 314 -- 6.9. Malliavin's method 316 -- 6.10. Surface measures 321 -- 6.11. Complements and problems 324 -- Chapter 7. Applications 333 -- 7.1. Trajectories of Gaussian processes 333 -- 7.2. Infinite dimensional Wiener processes 336 -- 7.3. Logarithmic gradients 339 -- 7.4. Spherically symmetric measures 344 -- 7.5. Infinite dimensional diffusions 346 -- 7.6. Complements and problems 353 -- Appendix A. Locally Convex Spaces, Operators, and Measures 361 -- A.1. Locally convex spaces 361 -- A.2. Linear operators 365 -- A.3. Measures and measurability 371.".
catalog title "Gaussian measures / Vladimir I. Bogachev.".
catalog title "Gaussovskie mery. English".
catalog type "text".