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1. Probability : theory and examples [2019]
- Durrett, Richard, 1951- author.
- Fifth edition - Cambridge ; New York, NY : Cambridge University Press, 2019
- Description
- Book — 1 online resource
- Summary
-
- 1. Measure theory--
- 2. Laws of large numbers--
- 3. Central limit theorems--
- 4. Martingales--
- 5. Markov chains--
- 6. Ergodic theorems--
- 7. Brownian motion--
- 8. Applications to random walk--
- 9. Multidimensional Brownian motion-- Appendix. Measure theory details.
- (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
2. 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
3. Probability and measure [2012]
- Billingsley, Patrick.
- Anniversary ed - Hoboken, N.J. : Wiley, ©2012
- Description
- Book — 1 online resource (xvii, 624 pages) : illustrations
- Summary
-
- FOREWORD xi PREFACE xiii Patrick Billingsley 1925
- 2011 xv Chapter1 PROBABILITY 1
- 1. BOREL S NORMAL NUMBER THEOREM, 1 The Unit Interval The Weak Law of Large Numbers The Strong Law of Large Numbers Strong Law Versus Weak Length The Measure Theory of Diophantine Approximation*
- 2. PROBABILITY MEASURES, 18 Spaces Assigning Probabilities Classes of Sets Probability Measures Lebesgue Measure on the Unit Interval Sequence Space* Constructing s-Fields*
- 3. EXISTENCE AND EXTENSION, 39 Construction of the Extension Uniqueness and the p ? Theorem Monotone Classes Lebesgue Measure on the Unit Interval Completeness Nonmeasurable Sets Two Impossibility Theorems*
- 4. DENUMERABLE PROBABILITIES, 53 General Formulas Limit Sets Independent Events Subfields The Borel-Cantelli Lemmas The Zero-One Law
- 5. SIMPLE RANDOM VARIABLES, 72 Definition Convergence of Random Variables Independence Existence of Independent Sequences Expected Value Inequalities
- 6. THE LAW OF LARGE NUMBERS, 90 The Strong Law The Weak Law Bernstein's Theorem A Refinement of the Second Borel-Cantelli Lemma
- 7. GAMBLING SYSTEMS, 98 Gambler's Ruin Selection Systems Gambling Policies Bold Play* Timid Play*
- 8. MARKOV CHAINS, 117 Definitions Higher-Order Transitions An Existence Theorem Transience and Persistence Another Criterion for Persistence Stationary Distributions Exponential Convergence* Optimal Stopping*
- 9. LARGE DEVIATIONS AND THE LAW OF THE ITERATED LOGARITHM, 154 Moment Generating Functions Large Deviations Chernoff's Theorem* The Law of the Iterated Logarithm Chapter2 MEASURE 167
- 10. GENERAL MEASURES, 167 Classes of Sets Conventions Involving 8 Measures Uniqueness
- 11. OUTER MEASURE, 174 Outer Measure Extension An Approximation Theorem
- 12. MEASURES IN EUCLIDEAN SPACE, 181 Lebesgue Measure Regularity Specifying Measures on the Line Specifying Measures in Rk Strange Euclidean Sets*
- 13. MEASURABLE FUNCTIONS AND MAPPINGS, 192 Measurable Mappings Mappings into Rk Limits and Measurability Transformations of Measures
- 14. DISTRIBUTION FUNCTIONS, 198 Distribution Functions Exponential Distributions Weak Convergence Convergence of Types* Extremal Distributions* Chapter3 INTEGRATION 211
- 15. THE INTEGRAL, 211 Definition Nonnegative Functions Uniqueness
- 16. PROPERTIES OF THE INTEGRAL, 218 Equalities and Inequalities Integration to the Limit Integration over Sets Densities Change of Variable Uniform Integrability Complex Functions
- 17. THE INTEGRAL WITH RESPECT TO LEBESGUE MEASURE, 234 The Lebesgue Integral on the Line The Riemann Integral The Fundamental Theorem of Calculus Change of Variable The Lebesgue Integral in Rk Stieltjes Integrals
- 18. PRODUCT MEASURE AND FUBINI S THEOREM, 245 Product Spaces Product Measure Fubini's Theorem Integration by Parts Products of Higher Order
- 19. THE Lp SPACES*, 256 Definitions Completeness and Separability Conjugate Spaces Weak Compactness Some Decision Theory The Space L2 An Estimation Problem Chapter4 RANDOM VARIABLES AND EXPECTED VALUES 271
- 20. RANDOM VARIABLES AND DISTRIBUTIONS, 271 Random Variables and Vectors Subfields Distributions Multidimensional Distributions Independence Sequences of Random Variables Convolution Convergence in Probability The Glivenko-Cantelli Theorem*
- 21. EXPECTED VALUES, 291 Expected Value as Integral Expected Values and Limits Expected Values and Distributions Moments Inequalities Joint Integrals Independence and Expected Value Moment Generating Functions
- 22. SUMS OF INDEPENDENT RANDOM VARIABLES, 300 The Strong Law of Large Numbers The Weak Law and Moment Generating Functions Kolmogorov's Zero-One Law Maximal Inequalities Convergence of Random Series Random Taylor Series*
- 23. THE POISSON PROCESS, 316 Characterization of the Exponential Distribution The Poisson Process The Poisson Approximation Other Characterizations of the Poisson Process Stochastic Processes
- 24. THE ERGODIC THEOREM*, 330 Measure-Preserving Transformations Ergodicity Ergodicity of Rotations Proof of the Ergodic Theorem The Continued-Fraction Transformation Diophantine Approximation Chapter5 CONVERGENCE OF DISTRIBUTIONS 349
- 25. WEAK CONVERGENCE, 349 Definitions Uniform Distribution Modulo 1* Convergence in Distribution Convergence in Probability Fundamental Theorems Helly's Theorem Integration to the Limit
- 26. CHARACTERISTIC FUNCTIONS, 365 Definition Moments and Derivatives Independence Inversion and the Uniqueness Theorem The Continuity Theorem Fourier Series*
- 27. THE CENTRAL LIMIT THEOREM, 380 Identically Distributed Summands The Lindeberg and Lyapounov Theorems Dependent Variables*
- 28. INFINITELY DIVISIBLE DISTRIBUTIONS*, 394 Vague Convergence The Possible Limits Characterizing the Limit
- 29. LIMIT THEOREMS IN Rk, 402 The Basic Theorems Characteristic Functions Normal Distributions in Rk The Central Limit Theorem
- 30. THE METHOD OF MOMENTS*, 412 The Moment Problem Moment Generating Functions Central Limit Theorem by Moments Application to Sampling Theory Application to Number Theory Chapter6 DERIVATIVES AND CONDITIONAL PROBABILITY 425
- 31. DERIVATIVES ON THE LINE*, 425 The Fundamental Theorem of Calculus Derivatives of Integrals Singular Functions Integrals of Derivatives Functions of Bounded Variation
- 32. THE RADON NIKODYM THEOREM, 446 Additive Set Functions The Hahn Decomposition Absolute Continuity and Singularity The Main Theorem
- 33. CONDITIONAL PROBABILITY, 454 The Discrete Case The General Case Properties of Conditional Probability Difficulties and Curiosities Conditional Probability Distributions
- 34. CONDITIONAL EXPECTATION, 472 Definition Properties of Conditional Expectation Conditional Distributions and Expectations Sufficient Subfields* Minimum-Variance Estimation*
- 35. MARTINGALES, 487 Definition Submartingales Gambling Functions of Martingales Stopping Times Inequalities Convergence Theorems Applications: Derivatives Likelihood Ratios Reversed Martingales Applications: de Finetti's Theorem Bayes Estimation A Central Limit Theorem* Chapter7 STOCHASTIC PROCESSES 513
- 36. KOLMOGOROV'S EXISTENCE THEOREM, 513 Stochastic Processes Finite-Dimensional Distributions Product Spaces Kolmogorov's Existence Theorem The Inadequacy of RT A Return to Ergodic Theory The Hewitt Savage Theorem*
- 37. BROWNIAN MOTION, 530 Definition Continuity of Paths Measurable Processes Irregularity of Brownian Motion Paths The Strong Markov Property The Reflection Principle Skorohod Embedding Invariance*
- 38. NONDENUMERABLE PROBABILITIES, 558 Introduction Definitions Existence Theorems Consequences of Separability*
- APPENDIX 571 NOTES ON THE PROBLEMS 587 BIBLIOGRAPHY 617 INDEX 619.
- (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
Online 4. Probability : theory and examples [2010]
- Durrett, Richard, 1951-
- 4th ed. - Cambridge ; New York : Cambridge University Press, 2010.
- Description
- Book — x, 428 p. : ill. ; 27 cm.
- Summary
-
- 1. Measure theory--
- 2. Laws of large numbers--
- 3. Central limit theorems--
- 4. Random walks--
- 5. Martingales--
- 6. Markov chains--
- 7. Ergodic theorems--
- 8. Brownian motion-- Appendix A. Measure theory details.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
- Also online at
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA273 .D865 2010 | 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
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
8. Probability with martingales [1991]
- Williams, D. (David), 1938-
- Cambridge ; New York : Cambridge University Press, c1991.
- Description
- Book — xv, 251 p. ; 23 cm.
- Summary
-
- 1. A branching-process example-- Part I. Foundations:
- 2. Measure spaces--
- 3. Events--
- 4. Random variables--
- 5. Independence--
- 6. Integration--
- 7. Expectation--
- 8. An easy strong law: product measure-- Part II. Martingale Theory:
- 9. Conditional expectation--
- 10. Martingales--
- 11. The convergence theorem--
- 12. Martingales bounded in L2--
- 13. Uniform integrability--
- 14. UI martingales--
- 15. Applications-- Part III. Characteristic Functions:
- 16. Basic properties of CFs--
- 17. Weak convergence--
- 18. The central limit theorem-- Appendices-- Exercises.
- (source: Nielsen Book Data)
(source: Nielsen Book Data)
Green Library, Science Library (Li and Ma)
Green Library | Status |
---|---|
Find it Stacks | Request (opens in new tab) |
QA274.5 .W55 1991 | Unknown |
Science Library (Li and Ma) | Status |
---|---|
Stacks | Request (opens in new tab) |
QA274.5 .W55 1991 | Unknown |
MATH-230B-01, STATS-305B-01, STATS-310B-01
- Course
- MATH-230B-01 -- Theory of Probability
- Instructor(s)
- Dembo, Amir
- Course
- STATS-305B-01 -- Applied Statistics II
- Instructor(s)
- Efron, Bradley
- Course
- STATS-310B-01 -- Theory of Probability II
- Instructor(s)
- Dembo, Amir