Probability
Theory
Summary [html].
- E. T. Jaynes, ``PROBABILITY
THEORY: THE LOGIC OF SCIENCE,'' Cambridge University Press
(June 9, 2003)
- Joseph E. Yukich, ``Probability theory of classical Euclidean optimization problems,''
Berlin; New York: Springer, 1998.
- Athanasios Papoulis, ``Probability, random variables, and stochastic processes,''
3rd ed., New York : McGraw-Hill, c1991.
- W. Feller, An Introduction to Probability Theory and Its Applications , John Wiley
& Sons, 1971.
- K.L. Chung, A Course in Probability Theory, Academic Press, 2001.
- P. Whittle, Probability via Expectations, Springer-Verlag, 2000.
- P. Billingsley, Probability and Measure, John Wiley, 1995.
- P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, 1999.
- Hermann Thorisson, Coupling, Stationarity, and Regeneration, Springer Verlag 2000.
- S. I. Resnick, A Probability Path, Birkauser, 2001.
- J. Patel, C. Kapadia, and D. Owen,
Handbook of Statistical Distributions, Marcel Dekker, NY, 1976.
- H. Stark and J.W. Woods, Probability Theory,
Random Processes, and Estimation Theory for Engineers, Prentice Hall, 1994.
- Y. S. Chow, H. Teicher, "Probability theory:
independence, interchangeability, martingales," 2 ed., Springer, 1988.
Mathematical/Theoretical
Statistics
- Sara A. van de Geer, ``Applications of empirical process theory,'' Cambridge University Press, 2000.
- Robert S. Liptser, Albert N. Shiryaev, ``Statistics of random processes,''
translated by A.B. Aries; translation editor, Stephen S. Wilson. 2nd
edition, Vols. I (Theory) and II (Applications). Springer, 2001.
- A.A. Borovkov, ``Ergodicity and stability of stochastic processes,''
translated by V. Yurinsky, Chichester [England]; New York: Wiley,
1998.
- Lucien Le Cam, Grace Lo Yang, ``Asymptotics in statistics : some basic concepts,'' 2nd ed.,
New York : Springer, 2000.
- D. R. Cox, ``Theoretical statistics''.
- Ulrich Krengel, ``Ergodic Theorems,'' 1985. Walter de Gruyter, Inc.; ISBN: 3110084783; (July 1985).
- E.L. Lehmann,``Theory
of point estimation,''2nd ed., New York : Springer, c1998.
- E.L. Lehmann,``Testing statistical hypotheses,''2nd ed., New York : Wiley,
c1986.
- Silvey, S. "Statistical Inference".
- Bickel, P. and Doksum, K. "Mathematical Statistics".
Applied
Statistics
Summary [html].
- Glen McPherson, ``Applying and interpreting statistics : a comprehensive guide,''
2nd ed., New York : Springer, 2001. (user's perspective)
- Robert V. Hogg and Johannes Ledolter,
``Engineering statistics,'' New York : Macmillan ; London : Collier Macmillan,
1987.
- F. R. Hampel, P.J. Rosseeuw, E. M. Ronchetti, and W. A.
Stahel, Robust Statistics: The Approach Based on Influence Functions, John Wiley and Sons, 1986.
- Murray R. Spiegel, Larry J. Stephens, ``Schaum's Outline of Statistics,'' 3rd
ed., McGraw-Hill, 1998.
Stochastic
Process
Summary [doc].
- Howard M. Taylor, Samuel Karlin, ``An introduction to stochastic modeling,''
3rd ed., San Diego: Academic Press, 1998.
- L.C.G. Rogers and David Williams, ``Diffusions, Markov processes, and martingales,''
2nd ed., Cambridge, U.K.; New York: Cambridge University Press, 2000.
- Robert M. Gray, ``Probability, random processes, and ergodic properties,''
New York : Springer-Verlag, 1988.
- Robert M. Gray, Lee D. Davisson, ``Random processes : a mathematical approach for engineers,''
Englewood Cliffs, N.J. : Prentice-Hall, c1986.
- S. M. Ross, Introduction to Probability Models, Any Edition, Academic Press, 1997.
- S. M. Ross, Stochastic Processes, Any Edition, John Wiley, 1996.
- R. G. Gallager, Discrete Stochastic Processes , Kluwer Academic Publishers, 1996.
- S. Karlin and H. M. Taylor, A First Course in Stochastic Processes , Academic Press, 1975.
- Sidney I. Resnick, Adventures in Stochastic Processes, Birkhauser, 1992.
- E. Cinlar, Introduction to Stochastic Processes, Prentice-Hall, Inc., 1975.
- D. R. Cox, Renewal Theory.
Statistical Inference
- G. Casella and R. L. Berger, Statistical Inference,
Duxburry, 2002.
- O.E. Barndorff-Nielsen, D.R. Cox, ``Inference and Asymptotics,''
CRC Press, 1994.
- Ishwar V. Basawa and B.L.S. Prakasa Rao,
``Statistical inference for stochastic processes,'' London ; New York : Academic Press, 1980.
- B.L.S. Prakasa Rao, ``Asymptotic theory of statistical inference,''
New York : Wiley, c1987.
- Masanobu Taniguchi, Yoshihide Kakizawa, ``Asymptotic theory of statistical inference for time series,''
New York : Springer, c2000.
- B.L.S. Prakasa Rao, ``Nonparametric functional estimation,''
Orlando : Academic Press, 1983.
- Bayesian inference and maximum entropy methods in science and engineering : 20th international workshop,
Gif-sur-Yvette, France, 8-13 July 2000 / editor, Ali Mohammad-Djafari. Publication info: Melville, N.Y. : American Institute of Physics, 2001.
- Bayesian inference and maximum entropy methods in science and engineering : 19th international workshop, Boise, Idaho, 2-5
August 1999 / editors, Joshua T. Rychert, Gary J. Erickson, C. Ray Smith. Publication info:
Melville, N.Y. : American Institute of Physics, 2001.
Large
Deviation Theory
Summary [doc].
- Paul Dupuis and Richard S. Ellis, ``A weak convergence approach to the theory of large deviations,''
New York : Wiley, 1997.
- Jean-Dominique Deuschel, Daniel W. Stroock,
``Large deviations,'' Boston : Academic Press, 1989.
- Richard S. Ellis, ``Entropy, large deviations, and statistical mechanics,''
New York, N.Y. : Springer-Verlag, 1985.
- D.W. Stroock, ``An introduction to the theory of large deviations,''
New York : Spring-Verlag, 1984.
- A. Shwartz and A. Weiss, ``Large deviations
for performance analysis,'' New York: Chapman and Hall, 1995.
- A. Dembo and O. Zeitouni, ``Large deviations
techniques and applications,'' Boston: Jones and Bartlett, 1992.
- M. I. Freidlin and A. D. Wentzell, ``Random
perturbations of dynamical systems,'' New York : Springer-Verlag,
1984.
- S. R. S. Varadhan, ``Large deviations and
applications,'' Philadelphia, PA: SIAM, 1984.
- J. A. Bucklew, ``Large deviations techniques
in decision and estimation,'' New York : Wiley,
1990.
- A. D. Wentzell, ``Limit theorems on large
deviations for Markov statistic processes,'' Dordecht, Holland: Kluwer,
1990.
Self
similar processes
- R. Adler, R. Feldman, M. Taqqu (Eds), A
Practical Guide to Heavy Tails: Statistical Techniques for Analysing Heavy
Tailed Distributions, Birkhäuser, 1998.
- Gennady Samorodnitsky and Murad S. Taqqu,
"Stable Non-Gaussian Random Processes: Stochastic Models with Infinite
Variance", Chapman & Hall/CRC, 1994. ISBN: 0-412-05171-0.
- Jan Beran, Statistics for Long-Memory
Processes, Chapman & Hall/CRC, 1994. ISBN: 0-412-04901-5.
- E. Eberlein and M.S. Taqqu, editors,
"Dependence in Probability and Statistics: A Survey of Recent Results,"
Progress in Probability and Statistics Series, Vol. 11. ISBN 0-8176-3323-5.
Birkhäuser, Boston (1986).
- K. Park and W. Willinger, (ed.), Self-Similar
Network Traffic and Performance Evaluation, Wiley-Interscience, 2000
Time Series
Summary [html].
- Peter J. Brockwell, Richard A. Davis, ``Time series : theory and methods,''
2nd ed., New York : Springer-Verlag, c1991.
- George E.P. Box, Gwilym M. Jenkins, Gregory C.
Reinsel, ``Time series analysis : forecasting and control,'' 3rd ed., Englewood Cliffs, N.J. : Prentice Hall, c1994.
- Peter Bloomfield, ``Fourier analysis of time series : an introduction,'' 2nd ed. New York : Wiley,
2000.
- Smoothing and regression : approaches, computation, and application,
edited by Michael G. Schimek. New York : Wiley, 2000.
Monte Carlo
Methods
Summary [html].
- Christian P. Robert, George
Casella, ``Monte Carlo statistical methods,'' New York: Springer, 1999.
- Jun S. Liu, ``Monte Carlo strategies in
scientific computing,'' New York: Springer, 2001.
- Michael Evans and Tim Swartz, ``Approximating
integrals via Monte Carlo and deterministic methods,'' Oxford ; New York :
Oxford University Press, 2000.
- George S. Fishman, ``Monte Carlo : concepts,
algorithms, and applications,'' Corrected 3rd printing, New York : Springer,
1999.
- James E. Gentle, ``Random number generation
and Monte Carlo methods,'' New York : Springer, c1998.
- Dani Gamerman, ``Markov chain Monte Carlo :
stochastic simulation for Bayesian inference,'' 1st ed., London ; New York :
Chapman & Hall, 1997.
- G.A. Mikhailov ; translated by K.K. Sabelfeld,
``Optimization of weighted Monte Carlo methods,'' Berlin ; New York :
Springer-Verlag, 1992.
- Reuven Y. Rubinstein, ``Monte Carlo
optimization, simulation, and sensitivity of queueing networks,'' New York :
Wiley, c1986.
- Arnaud Doucet (Editor), Nando De Freitas
(Editor), Neil Gordon (Editor), Adrian Smith, ``Sequential Monte Carlo Methods
in Practice,''Springer Verlag; ISBN: 0387951466; (June 21, 2001)
- W.R. Gilks, S. Richardson and D.J.
Spiegelhalter (eds.), Markov Chain Monte Carlo in Practice, Chapman & Hall/CRC,
1996. ISBN: 0-412-05551-1.
- P. Bratley, B.L. Fox, L.E. Schrage, "A Guide
to Simulation," 2nd Ed. Springer-Verlag, New York, 1987.
- P. Br¨¦maud, "Markov Chains Gibbs Fields,
Monte Carlo Simulation, and Queues," Springer-Verlag, New York, 1999.
- M.-H. Chen, J.G. Ibrahim, Q.-M. Shao, "Monte
Carlo Methods in Bayesian Computation," New York, 2000.
Statistical Calculus
- J. Michael Steele, ``Stochastic Calculus and Financial Applications,'' Springer
Verlag,
2000.
- Robert J. Elliott, ``Stochastic calculus and applications,''
New York: Springer, 1982.
- Ioannis Karatzas, Steven E. Shreve, ``Brownian Motion and Stochastic Calculus,''
2nd ed., Springer, 1997.
- Philip E. Protter, ``Stochastic integration and differential equations: a new approach,''
2nd ed., Springer, 1990.
- Fima C. Klebaner, ``Introduction to Stochastic Calculus with Applications,'' Imperial College Press,
1999.
- Joel E. Cohen, J.H.B. Kemperman, Gh. Zbaganu,
``Comparisons of stochastic matrices, with applications in information theory, statistics, economics, and population sciences,''
Boston: Birkhäuser, 1998.
- Xuerong Mao, ``Exponential stability of stochastic differential equations,''
New York: M. Dekker, 1994.
- Thomas C. Gard, ``Introduction to stochastic differential equations,''
New York: M. Dekker, 1988.
Random graph
- Peter Hall, "Introduction to the Theory of
Coverage Processes," John Wiley & Sons Inc (October, 1988), ISBN: 0471857025
- Ronald Meester, Rahul Roy, "Continuum
Percolation," Cambridge University Press (June 13, 1996) ISBN:
052147504X
- Geoffrey Grimmett, "Percolation," Springer; 2
edition (June 11, 1999), ISBN: 3540649026
- Dietrich Stoyan, Wilfrid S. Kendall, Joseph
Mecke, "Stochastic Geometry and Its Applications," 2nd Edition, John Wiley &
Sons; 2 edition (July 18, 1996), ISBN: 0471950998
- Mathew Penrose, "Random Geometric Graphs,"
Oxford University Press (June 1, 2003), ISBN: 0198506260
Graphical model
- David Edwards, "Introduction to Graphical
Modelling," Springer; 2 edition (June 15, 2000) ISBN: 0387950540
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