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Online 1. 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)
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 Also online at
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  Request (opens in new tab) 
QA273 .D865 2010  Unknown 
MATH230B01, STATS310B01
 Course
 MATH230B01  Theory of Probability
 Instructor(s)
 Dembo, Amir
 Course
 STATS310B01  Theory of Probability II
 Instructor(s)
 Dembo, Amir
2. 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.
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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  Request (opens in new tab) 
QA300 .D83 2002  Unknown 
MATH230B01, STATS310B01
 Course
 MATH230B01  Theory of Probability
 Instructor(s)
 Dembo, Amir
 Course
 STATS310B01  Theory of Probability II
 Instructor(s)
 Dembo, Amir
3. 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 branchingprocess 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.
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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 
MATH230B01, STATS305B01, STATS310B01
 Course
 MATH230B01  Theory of Probability
 Instructor(s)
 Dembo, Amir
 Course
 STATS305B01  Applied Statistics II
 Instructor(s)
 Efron, Bradley
 Course
 STATS310B01  Theory of Probability II
 Instructor(s)
 Dembo, Amir