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1. Real analysis and probability [2018]
- Dudley, R. M. (Richard M.), author.
- Boca Raton, Fla. : CRC Press, 2018
- Description
- Book — 1 online resource (xi, 176 pages)
- Summary
-
- chapter 1 Foundations; Set Theory / Richard M. Dudley
- chapter 2 General Topology / Richard M. Dudley
- chapter 3 Measures / Richard M. Dudley
- chapter 4 Integration / Richard M. Dudley
- chapter 5 Lp Spaces; Introduction to Functional Analysis / Richard M. Dudley
- chapter 6 Convex Sets and Duality of Normed Spaces / Richard M. Dudley
- chapter 7 Measure, Topology, and Differentiation / Richard M. Dudley
- chapter 8 Introduction to Probability Theory / Richard M. Dudley
- chapter 9 Convergence of Laws and Central Limit Theorems / Richard M. Dudley
- chapter 10 Conditional Expectations and Martingales / Richard M. Dudley
- chapter 11 Convergence of Laws on Separable Metric Spaces / Richard M. Dudley
- chapter 12 Stochastic Processes / Richard M. Dudley
- chapter 13 Measurability: Borel Isomorphism and Analytic Sets / Richard M. Dudley
(source: Nielsen Book Data)
MATH-230B-01, STATS-310B-01
- Course
- MATH-230B-01 -- Theory of Probability
- Instructor(s)
- Dembo, Amir
- Course
- STATS-310B-01 -- Theory of Probability II
- Instructor(s)
- Dembo, Amir
2. Uniform central limit theorems [2014]
- Dudley, R. M. (Richard M.)
- Second edition. - New York : Cambridge University Press, 2014.
- Description
- Book — xii, 472 pages ; 23 cm.
- Summary
-
- 1. Donsker's theorem and inequalities--
- 2. Gaussian processes, sample continuity--
- 3. Definition of Donsker classes--
- 4. Vapnik-Cervonenkis combinatorics--
- 5. Measurability--
- 6. Limit theorems for VC-type classes--
- 7. Metric entropy with bracketing--
- 8. Approximation of functions and sets--
- 9. Two samples and the bootstrap--
- 10. Uniform and universal limit theorems--
- 11. Classes too large to be Donsker-- Appendix A. Differentiating under an integral sign-- Appendix B. Multinomial distributions-- Appendix C. Measures on nonseparable metric spaces-- Appendix D. An extension of Lusin's theorem-- Appendix E. Bochner and Pettis integrals-- Appendix F. Non-existence of some linear forms-- Appendix G. Separation of analytic sets-- Appendix H. Young-Orlicz spaces--
- Appendix I. Versions of isonormal processes.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA273.67 .D84 2014 | Unknown |
3. Concrete functional calculus [2011]
- Dudley, R. M. (Richard M.)
- New York : Springer, ©2011.
- Description
- Book — 1 online resource (xii, 667 pages).
- Summary
-
- Preface
- 1 Introduction and Overview
- 2 Definitions and Basic Properties of Extended Riemann-Stieltjes Integrals
- 3 Phi-variation and p-variation; Inequalities for Integrals
- 4 Banach Algebras
- 5 Derivatives and Analyticity in Normed Spaces
- 6 Nemytskii Operators on Some Function Spaces
- 7 Nemytskii Oerators on Lp Spaces
- 8 Two-Function Composition
- 9 Product Integration
- 10 Nonlinear Differential and Integral Equations
- 11 Fourier Series
- 12 Stochastic Processes and Phi-Variation
- Appendix Nonatomic Measure Spaces
- References
- Subject Index
- Author Index
- Index of Notation.
4. Selected works of R.M. Dudley [2010]
- Dudley, R. M. (Richard M.)
- New York ; London : Springer, ©2010.
- Description
- Book — 1 online resource (xxiv, 481 pages).
- Summary
-
- Convergence in Law.- Weak Convergence of Probabilities on Nonseparable Metric Spaces and Empirical Measures on Euclidean Spaces.- Measures on Non-Separable Metric Spaces.- Distances of Probability Measures and Random Variables.- An Extended Wichura Theorem, Definitions of Donsker Class, and Weighted Empirical Distributions.- Markov Processes.- Lorentz-invariant Markov processes in relativistic phase space.- A note on Lorentz-invariant Markov processes.- Asymptotics of Some Relativistic Markov Processes.- Gaussian Processes.- The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes.- On seminorms and probabilities, and abstract Wiener spaces.- Sample Functions of the Gaussian Process.- On the Lower Tail of Gaussian Seminorms.- Empirical Processes.- Special Invited Paper.- Empirical and Poisson Processes on Classes of Sets or Functions Too Large for Central Limit Theorems.- Invariance Principles for Sums of Banach Space Valued Random Elements and Empirical Processes.- Universal Donsker Classes and Metric Entropy.- Nonlinear functionals and p-variation.- Frechet Differentiability, p-Variation and Uniform Donsker Classes.- The Order of the Remainder in Derivatives of Composition and Inverse Operators for p-Variation Norms.- Empirical Processes and p-variation.- Miscellanea.- Pathological Topologies and Random Walks on Abelian Groups.- Metric Entropy of Some Classes of Sets with Differentiable Boundaries.- Wiener Functionals as Ito Integrals.- A Metric Entropy Bound is Not Sufficient for Learnability.- Asymptotic Normality with Small Relative Errors of Posterior Probabilities of Half-Spaces.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
5. Real analysis and probability [2002]
- Dudley, R. M. (Richard M.)
- Cambridge ; New York : Cambridge University Press, 2002.
- Description
- Book — x, 555 p. ; 24 cm.
- Summary
-
- 1. Foundations: set theory--
- 2. General topology--
- 3. Measures--
- 4. Integration--
- 5. Lp spaces: introduction to functional analysis--
- 6. Convex sets and duality of normed spaces--
- 7. Measure, topology, and differentiation--
- 8. Introduction to probability theory--
- 9. Convergence of laws and central limit theorems--
- 10. Conditional expectations and martingales--
- 11. Convergence of laws on separable metric spaces--
- 12. Stochastic processes--
- 13. Measurability: Borel isomorphism and analytic sets-- Appendixes: A. Axiomatic set theory-- B. Complex numbers, vector spaces, and Taylor's theorem with remainder-- C. The problem of measure-- D. Rearranging sums of nonnegative terms-- E. Pathologies of compact nonmetric spaces-- Indices.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA300 .D83 2002 | Unknown |
MATH-230B-01, STATS-310B-01
- Course
- MATH-230B-01 -- Theory of Probability
- Instructor(s)
- Dembo, Amir
- Course
- STATS-310B-01 -- Theory of Probability II
- Instructor(s)
- Dembo, Amir
6. Real analysis and probability [2002]
- Dudley, R. M. (Richard M.)
- Cambridge ; New York : Cambridge University Press, 2002.
- Description
- Book — 1 online resource (x, 555 pages).
- Summary
-
- 1. Foundations: set theory--
- 2. General topology--
- 3. Measures--
- 4. Integration--
- 5. Lp spaces: introduction to functional analysis--
- 6. Convex sets and duality of normed spaces--
- 7. Measure, topology, and differentiation--
- 8. Introduction to probability theory--
- 9. Convergence of laws and central limit theorems--
- 10. Conditional expectations and martingales--
- 11. Convergence of laws on separable metric spaces--
- 12. Stochastic processes--
- 13. Measurability: Borel isomorphism and analytic sets-- Appendixes: A. Axiomatic set theory-- B. Complex numbers, vector spaces, and Taylor's theorem with remainder-- C. The problem of measure-- D. Rearranging sums of nonnegative terms-- E. Pathologies of compact nonmetric spaces-- Indices.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
MATH-230B-01, STATS-310B-01
- Course
- MATH-230B-01 -- Theory of Probability
- Instructor(s)
- Dembo, Amir
- Course
- STATS-310B-01 -- Theory of Probability II
- Instructor(s)
- Dembo, Amir
- Dudley, R. M. (Richard M.)
- Cambridge ; New York : Cambridge University Press, 2002.
- Description
- Book — x, 555 p.
- Summary
-
- 1. Foundations: set theory--
- 2. General topology--
- 3. Measures--
- 4. Integration--
- 5. Lp spaces: introduction to functional analysis--
- 6. Convex sets and duality of normed spaces--
- 7. Measure, topology, and differentiation--
- 8. Introduction to probability theory--
- 9. Convergence of laws and central limit theorems--
- 10. Conditional expectations and martingales--
- 11. Convergence of laws on separable metric spaces--
- 12. Stochastic processes--
- 13. Measurability: Borel isomorphism and analytic sets-- Appendixes: A. Axiomatic set theory-- B. Complex numbers, vector spaces, and Taylor's theorem with remainder-- C. The problem of measure-- D. Rearranging sums of nonnegative terms-- E. Pathologies of compact nonmetric spaces-- Indices.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
MATH-230B-01, STATS-310B-01
- Course
- MATH-230B-01 -- Theory of Probability
- Instructor(s)
- Dembo, Amir
- Course
- STATS-310B-01 -- Theory of Probability II
- Instructor(s)
- Dembo, Amir
- Dudley, R. M. (Richard M.)
- Berlin ; London : Springer, c1999.
- Description
- Book — vii, 277 p. ; 24 cm.
- Summary
-
- Preface.- A survey on differentiability of six operators in relation to probability and statistics.- Product integrals, Young integrals and p-variation.- Differentiability of the composition and inverse operators for regulated and a.e. continuous functions.- Bibliographies on p-variation and phi-variation.- Subject Index.- Author Index.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
SAL1&2 (on-campus shelving)
SAL1&2 (on-campus shelving) | Status |
---|---|
Serials | Request (opens in new tab) |
Shelved by Series title V.1703 | Unknown |
9. Uniform central limit theorems [1999]
- Dudley, R. M. (Richard M.)
- Cambridge ; New York : Cambridge University Press, 1999.
- Description
- Book — xiv, 436 p. : ill. ; 24 cm.
- Summary
-
- Preface--
- 1. Introduction: Donsker's theorem, metric entropy and inequalities--
- 2. Gaussian measures and processes-- sample continuity--
- 3. Foundations of uniform central limit theorems: Donsker classes--
- 4. Vapnik- ervonenkis combinatorics--
- 5. Measurability--
- 6. Limit theorems for Vapnik- ervonenkis and related classes--
- 7. Metric entropy, with inclusion and bracketing--
- 8. Approximation of functions and sets--
- 9. Sums in general Banach spaces and invariance principles--
- 10. Universal and uniform central limit theorems--
- 11. The two-sample case, the bootstrap, and confidence sets--
- 12. Classes of sets or functions too large for central limit theorems-- Appendices-- Subject index-- Author index-- Index of notation.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA273.67 .D84 1999 | Unknown |
10. Real analysis and probability [1989]
- Dudley, R. M. (Richard M.)
- Pacific Grove, Calif. : Brooks/Cole Pub. Co., 1989.
- Description
- Book — xi, 436 p. : ill. ; 24 cm.
- Summary
-
- Foundations: set theory. General topology. Measures. Integration. Lp spaces: introduction to functional analysis. Convex sets and duality of normed spaces. Measure, topology and differentiation. Introduction to probability theory. Convergence of laws and central limit theorems. Conditional expectation and martingales. Convergence of laws on separable metric spaces. Stochastic processes. Measurability: Borel isomorphism and analytic sets. Appendices.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
- Online
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA300 .D83 1989 | Unknown |
11. Probabilities and metrics : convergence of laws on metric spaces, with a view to statistical testing [1976]
- Dudley, R. M. (Richard M.)
- [Aarhus, Denmark] : Aarhus universitet, Matematisk institut, 1976.
- Description
- Book — [128] p. ; 21 cm.
- Online
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA1 .A13 NO.45 | Available |
- Boston : Birkhäuser, c1992.
- Description
- Book — xi, 510 p. ; 24 cm.
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA 273.43 .P773 1992 | Available |
- Ecole d'été de probabilités de Saint-Flour (12th : 1982)
- Berlin ; New York : Springer-Verlag, 1984.
- Description
- Book — x, 396 p. ; 25 cm.
SAL1&2 (on-campus shelving)
SAL1&2 (on-campus shelving) | Status |
---|---|
Serials | Request (opens in new tab) |
Shelved by Series title V.1097 | Unknown |
- Gaithersburg, MD : U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, Computer Security Division, Information Technology Laboratory, [2006]
- Description
- Book — 1 online resource (97 unnumbered pages) : illustrations.
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