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 Williams, D. (David), 1938
 Cambridge, U.K. ; New York : Cambridge University Press, 2001.
 Description
 Book — xvii, 547 p. : ill. ; 25 cm.
 Summary

 Preface
 1. Introduction
 2. Events and probabilities
 3. Random variables, means and variances
 4. Conditioning and independence
 5. Generating functions and the central limit theorem
 6. Confidence intervals for 1parameter models
 7. Conditional pdfs and multiparameter Bayesian statistics
 8. Linear models, ANOVA etc
 9. Some further probability
 10. Quantum probability and quantum computing Appendix A. Some prerequisites and addenda Appendix B. Discussion of some selected exercises Appendix C. Tables Appendix D. A small sample of the literature Bibliography Index.
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Marine Biology Library (Miller), Science Library (Li and Ma)
Marine Biology Library (Miller)  Status 

Stacks  
QA273 .W626 2001  Unknown 
Science Library (Li and Ma)  Status 

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QA273 .W626 2001  Unknown 
2. 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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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA274.5 .W55 1991  Unknown On reserve at Li and Ma Science Library 2hour loan 
QA274.5 .W55 1991  Unknown On reserve at Li and Ma Science Library 2day loan 
STATS310B01, MATH230B01
 Course
 STATS310B01  Theory of Probability II
 Instructor(s)
 Dembo, Amir
 Course
 MATH230B01  Theory of Probability
 Instructor(s)
 Dembo, Amir
3. Diffusions, Markov processes, and martingales [1979  ]
 Williams, D. (David), 1938
 Chichester ; New York : Wiley, c1979
 Description
 Book — v. ; 24 cm.
 Summary

 v. 1. Foundations.
 v. 2. Itô calculus.
 Online
Science Library (Li and Ma)
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QA274.7 .W54 V.1  Unknown 
QA274.7 .W54 V.2  Unknown 
 Rogers, L. C. G.
 2nd ed.  Cambridge, U.K. ; New York : Cambridge University Press, 2000.
 Description
 Book — 2 v. : ill. ; 23 cm.
 Summary

 Some frequently used notation
 1. Brownian motion Part I. Introduction
 2. Basics about Brownian motion
 3. Brownian motion in higher dimensions
 4. Gaussian processes and Levy processes Part II. Some Classical Theory
 5. Basic measure theory
 6. Basic probability theory
 7. Stochastic processes
 8. Discreteparameter martingale theory
 9. Continuousparameter martingale theory
 10. Probability measure on Lusin spaces Part III. Markov Processes:
 11. Transition functions and resolvents
 12. FellerDynkin processes
 13. Additive functionals
 14. Approach to ray processes: the Martin boundary
 15. Ray processes
 16. Applications References Index.
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 Some frequently used notation
 4. Introduction to Ito calculus 4.1. Some motivating remarks 4.2. Some fundamental ideas: previsible processes, localization, etc. 4.3. The elementary theory of finitevariation processes 4.4. Stochastic integrals: the L2 theory 4.5. Stochastic integrals with respect to continuous semimartingales 4.6. Applications of Ito's formula
 5. Stochastic differential equations and diffusions 5.1. Introduction 5.2. Pathwise uniqueness, strong SDEs, flows 5.3. Weak solutions, uniqueness in law 5.4. Martingale problems, Markov property 5.5. Overture to stochastic differential geometry 5.6. Onedimensional SDEs 5.7. Onedimensional diffusions
 6. The general theory 6.1. Orientation 6.2. Debut and section theorems 6.3. Optional projections and filtering 6.4. Characterising previsible times 6.5. Dual previsible projections 6.6. The Meyer decomposition theorem 6.7. Stochastic integration: the general case 6.8. Ito excursion theory References Index.
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This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
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QA274.7 .W54 2000 V.2  Unknown 
5. Diffusions, Markov processes, and martingales [1994  ]
 Rogers, L. C. G.
 2nd ed.  Chichester, West Sussex, England ; New York : Wiley, c1994
 Description
 Book — v. ; 24 cm.
 Summary

 v. 1. Foundations
 v. 2. Itô calculus
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Science Library (Li and Ma)
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QA274.7 .W54 1994 V.1  Unknown 
 LMS Durham Symposium (1980)
 Berlin ; New York : SpringerVerlag, 1981.
 Description
 Book — viii, 540 p. ; 24 cm.
SAL1&2 (oncampus shelving)
SAL1&2 (oncampus shelving)  Status 

Serials  Request 
Shelved by Series title V.851  Unknown 
 London : Royal Society, 1991.
 Description
 Book — 240 p., 1 leaf of plates : ill. (some col.) ; 25 cm.
 Summary

 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers  dissipation of energy in the locally isotropic turbulence, A.N. Kolmogorov Kolmogorov's hydrodynamic attractors, V.I. Arnol'd approximation of attractors, large eddy simulations and multiscale methods, R. Temam transition functions, paths and path integrals, D. Williams turbulent cascade and intermittency growth, R.H. Kraichnan random multifractals  negative dimensions and the resulting limitations of the thermodynamic formalism, B.B. Mandelbrot from global scaling, a la Kolmogorov, to local multifractal scaling in developed turbulence, U. Frisch structure and dynamics of homogenous turbulence models and simulations, ZS She, E. Jackson and S.A. Orszag the Kolomorogov spectrum and its oceanic cousins  a review, O.M. Phillips local isotropy of the smallest scales of turbulent scalar and velocity fields, C. Van Atta Kolmogorov similarity hypotheses for scalar fields  sampling intermittent turbulent mixing in the ocean and galaxy, C.H. Gibson on local isotropy of passive scalars in turbulent shear flows, K.R. Sreenivasan Kolmogorov's contributions to the physical and geometrical understanding of smallscale turbulence and recent developments, J.C.R. Hunt and J.C. Vassilicos Kolmogorov's twoequation model of turbulence, D.B. Spalding some applications of Kolmogorov's turbulence research in the field of combustion, K.N.C. Bray and R.S. Cant.
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SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

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QA911 .T84 1991  Available 
8. Minerals of Mexico [1987]
 Panczner, William D. (William David), 1938
 New York : Van Nostrand Reinhold, c1987.
 Description
 Book — xiii, 459 p., [8] p. of plates : ill. (some col.), maps ; 26 cm.
 Online
Earth Sciences Library (Branner)
Earth Sciences Library (Branner)  Status 

Stacks  
QE377.M6 P36 1987  Unknown 
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