Probability Theory

Summary [html].

  1. E. T. Jaynes, ``PROBABILITY THEORY: THE LOGIC OF SCIENCE,''   Cambridge University Press (June 9, 2003)
  2. Joseph E. Yukich, ``Probability theory of classical Euclidean optimization problems,'' Berlin; New York: Springer, 1998. 
  3. Athanasios Papoulis, ``Probability, random variables, and stochastic processes,'' 3rd ed., New York : McGraw-Hill, c1991.
  4. W. Feller, An Introduction to Probability Theory and Its Applications , John Wiley & Sons, 1971.
  5. K.L. Chung, A Course in Probability Theory, Academic Press, 2001. 
  6. P. Whittle, Probability via Expectations, Springer-Verlag, 2000. 
  7. P. Billingsley, Probability and Measure, John Wiley, 1995. 
  8. P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, 1999. 
  9. Hermann Thorisson, Coupling, Stationarity, and Regeneration, Springer Verlag 2000. 
  10. S. I. Resnick, A Probability Path, Birkauser, 2001.  
  11. J. Patel, C. Kapadia, and D. Owen, Handbook of Statistical Distributions, Marcel Dekker, NY, 1976.
  12. H. Stark and J.W. Woods, Probability Theory, Random Processes, and Estimation Theory for Engineers, Prentice Hall, 1994.
  13. Y. S. Chow, H. Teicher, "Probability theory: independence, interchangeability, martingales," 2 ed., Springer, 1988.

Mathematical/Theoretical Statistics

  1. Sara A. van de Geer, ``Applications of empirical process theory,'' Cambridge University Press, 2000. 
  2. 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.
  3. A.A. Borovkov, ``Ergodicity and stability of stochastic processes,'' translated by V. Yurinsky, Chichester [England]; New York: Wiley, 1998. 
  4. Lucien Le Cam, Grace Lo Yang, ``Asymptotics in statistics : some basic concepts,'' 2nd ed., New York : Springer, 2000. 
  5. D. R. Cox, ``Theoretical statistics''. 
  6. Ulrich Krengel, ``Ergodic Theorems,'' 1985. Walter de Gruyter, Inc.; ISBN: 3110084783; (July 1985).
  7. E.L. Lehmann,``Theory of point estimation,''2nd ed., New York : Springer, c1998.
  8. E.L. Lehmann,``Testing statistical hypotheses,''2nd ed., New York : Wiley, c1986.
  9. Silvey, S. "Statistical Inference".
  10. Bickel, P. and Doksum, K. "Mathematical Statistics".

Applied Statistics

Summary [html].

  1. Glen McPherson, ``Applying and interpreting statistics : a comprehensive guide,'' 2nd ed., New York : Springer, 2001.  (user's perspective)
  2. Robert V. Hogg and Johannes Ledolter,  ``Engineering statistics,'' New York : Macmillan ; London : Collier Macmillan, 1987. 
  3. 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. 
  4. Murray R. Spiegel, Larry J. Stephens, ``Schaum's Outline of Statistics,'' 3rd ed., McGraw-Hill, 1998.

Stochastic Process

Summary [doc].

  1. Howard M. Taylor, Samuel Karlin, ``An introduction to stochastic modeling,'' 3rd ed., San Diego: Academic Press, 1998. 
  2. L.C.G. Rogers and David Williams, ``Diffusions, Markov processes, and martingales,'' 2nd ed., Cambridge, U.K.; New York: Cambridge University Press, 2000.
  3. Robert M. Gray, ``Probability, random processes, and ergodic properties,'' New York : Springer-Verlag, 1988.
  4. Robert M. Gray, Lee D. Davisson, ``Random processes : a mathematical approach for engineers,'' Englewood Cliffs, N.J. : Prentice-Hall, c1986.
  5. S. M. Ross, Introduction to Probability Models, Any Edition, Academic Press, 1997. 
  6. S. M. Ross, Stochastic Processes, Any Edition, John Wiley, 1996. 
  7. R. G. Gallager, Discrete Stochastic Processes , Kluwer Academic Publishers, 1996. 
  8. S. Karlin and H. M. Taylor, A First Course in Stochastic Processes , Academic Press, 1975. 
  9. Sidney I. Resnick, Adventures in Stochastic Processes, Birkhauser, 1992. 
  10. E. Cinlar, Introduction to Stochastic Processes, Prentice-Hall, Inc., 1975. 
  11. D. R. Cox, Renewal Theory.     

Statistical Inference

  1. G. Casella and R. L. Berger, Statistical Inference, Duxburry, 2002.  
  2. O.E. Barndorff-Nielsen, D.R. Cox, ``Inference and Asymptotics,''  CRC Press, 1994.
  3. Ishwar V. Basawa and B.L.S. Prakasa Rao, ``Statistical inference for stochastic processes,'' London ; New York : Academic Press, 1980. 
  4. B.L.S. Prakasa Rao, ``Asymptotic theory of statistical inference,'' New York : Wiley, c1987. 
  5. Masanobu Taniguchi, Yoshihide Kakizawa, ``Asymptotic theory of statistical inference for time series,'' New York : Springer, c2000. 
  6. B.L.S. Prakasa Rao, ``Nonparametric functional estimation,'' Orlando : Academic Press, 1983. 
  7. 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. 
  8. 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].

  1. Paul Dupuis and Richard S. Ellis, ``A weak convergence approach to the theory of large deviations,''  New York : Wiley, 1997.  
  2. Jean-Dominique Deuschel, Daniel W. Stroock, ``Large deviations,'' Boston : Academic Press, 1989. 
  3. Richard S. Ellis, ``Entropy, large deviations, and statistical mechanics,'' New York, N.Y. : Springer-Verlag, 1985. 
  4. D.W. Stroock, ``An introduction to the theory of large deviations,'' New York : Spring-Verlag, 1984.
  5. A. Shwartz and A. Weiss, ``Large deviations for performance analysis,'' New York: Chapman and Hall, 1995.
  6. A. Dembo and O. Zeitouni, ``Large deviations techniques and applications,'' Boston: Jones and Bartlett, 1992.
  7. M. I. Freidlin and A. D. Wentzell, ``Random perturbations of dynamical systems,'' New York : Springer-Verlag, 1984. 
  8. S. R. S. Varadhan, ``Large deviations and applications,'' Philadelphia, PA: SIAM, 1984.
  9. J. A. Bucklew, ``Large deviations techniques in decision and estimation,'' New York : Wiley, 1990.  
  10. A. D. Wentzell, ``Limit theorems on large deviations for Markov statistic processes,'' Dordecht, Holland: Kluwer, 1990.

Self similar processes

  1. R. Adler, R. Feldman, M. Taqqu (Eds), A Practical Guide to Heavy Tails: Statistical Techniques for Analysing Heavy Tailed Distributions,  Birkhäuser, 1998.
  2. 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.
  3. Jan Beran, Statistics for Long-Memory Processes, Chapman & Hall/CRC, 1994. ISBN: 0-412-04901-5.
  4. 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).
  5. K. Park and W. Willinger, (ed.), Self-Similar Network Traffic and Performance Evaluation, Wiley-Interscience, 2000

Time Series   

Summary [html].

  1. Peter J. Brockwell, Richard A. Davis, ``Time series : theory and methods,'' 2nd ed., New York : Springer-Verlag, c1991. 
  2. 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. 
  3. Peter Bloomfield, ``Fourier analysis of time series : an introduction,'' 2nd ed. New York : Wiley, 2000.
  4. Smoothing and regression : approaches, computation, and application, edited by Michael G. Schimek.  New York : Wiley, 2000.

Monte Carlo Methods   

Summary [html].

  1. Christian P. Robert, George Casella, ``Monte Carlo statistical methods,'' New York: Springer, 1999.
  2. Jun S. Liu, ``Monte Carlo strategies in scientific computing,'' New York: Springer, 2001.
  3. Michael Evans and Tim Swartz, ``Approximating integrals via Monte Carlo and deterministic methods,'' Oxford ; New York : Oxford University Press, 2000.
  4. George S. Fishman, ``Monte Carlo : concepts, algorithms, and applications,'' Corrected 3rd printing, New York : Springer, 1999.
  5. James E. Gentle, ``Random number generation and Monte Carlo methods,'' New York : Springer, c1998.
  6. Dani Gamerman, ``Markov chain Monte Carlo : stochastic simulation for Bayesian inference,'' 1st ed., London ; New York : Chapman & Hall, 1997.
  7. G.A. Mikhailov ; translated by K.K. Sabelfeld, ``Optimization of weighted Monte Carlo methods,'' Berlin ; New York : Springer-Verlag, 1992.
  8. Reuven Y. Rubinstein, ``Monte Carlo optimization, simulation, and sensitivity of queueing networks,'' New York : Wiley, c1986.
  9. 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)
  10. 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.
  11. P. Bratley, B.L. Fox, L.E. Schrage, "A Guide to Simulation," 2nd Ed. Springer-Verlag, New York, 1987.
  12. P. Br¨¦maud, "Markov Chains Gibbs Fields, Monte Carlo Simulation, and Queues," Springer-Verlag, New York, 1999.
  13. M.-H. Chen, J.G. Ibrahim, Q.-M. Shao, "Monte Carlo Methods in Bayesian Computation," New York, 2000.

Statistical Calculus   

  1. J. Michael Steele, ``Stochastic Calculus and Financial Applications,'' Springer Verlag, 2000.
  2. Robert J. Elliott, ``Stochastic calculus and applications,'' New York: Springer, 1982.
  3. Ioannis Karatzas, Steven E. Shreve, ``Brownian Motion and Stochastic Calculus,'' 2nd ed., Springer, 1997.
  4. Philip E. Protter, ``Stochastic integration and differential equations: a new approach,'' 2nd ed., Springer, 1990.
  5. Fima C. Klebaner, ``Introduction to Stochastic Calculus with Applications,'' Imperial College Press, 1999.
  6. 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.
  7. Xuerong Mao, ``Exponential stability of stochastic differential equations,'' New York: M. Dekker, 1994. 
  8. Thomas C. Gard, ``Introduction to stochastic differential equations,'' New York: M. Dekker, 1988. 

Random graph  

  1. Peter Hall, "Introduction to the Theory of Coverage Processes," John Wiley & Sons Inc (October, 1988), ISBN: 0471857025
  2. Ronald Meester, Rahul Roy, "Continuum Percolation," Cambridge University Press (June 13, 1996) ISBN: 052147504X
  3. Geoffrey Grimmett, "Percolation," Springer; 2 edition (June 11, 1999), ISBN: 3540649026
  4. Dietrich Stoyan, Wilfrid S. Kendall, Joseph Mecke, "Stochastic Geometry and Its Applications," 2nd Edition, John Wiley & Sons; 2 edition (July 18, 1996), ISBN: 0471950998
  5. Mathew Penrose, "Random Geometric Graphs," Oxford University Press (June 1, 2003), ISBN: 0198506260

Graphical model

  1. David Edwards, "Introduction to Graphical Modelling," Springer; 2 edition (June 15, 2000) ISBN: 0387950540


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