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Probability (book list)

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This is a section of the Basic Math Library List


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13. Probability and Statistics
    Classical probability theory, limit theorems and large deviations. Combinatorial probability.
    Random walks. Interacting particle systems. Stochastic networks. Stochastic geometry. 
    Stochastic analysis. Random fields. Random matrices and free probability. 
    Connections with sections 3, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18.



General

Borel, Emile. Elements of the Theory of Probability Englewood Cliffs, NJ: Prentice Hall, 1965.

  • Cacoullos, T. Exercises in Probability New York, NY: Springer-Verlag, 1989.
  • David, F.N. Games, Gods, and Gambling New York, NY: Hafner Press, 1962.
  • Gani, J., ed. The Craft of Probabilistic Modelling: A Collection of Personal Accounts New York, NY: Springer-Verlag, 1986.
    • Gnanadesikan, Mrudulla; Scheaffer, Richard L.; and Swift, Jim. The Art and Techniques of Simulation Palo Alto, CA: Dale Seymour, 1987.

Huff, Darrell and Geis, I. How to Take a Chance New York, NY: W.W. Norton, 1959.

  • Kahneman, Daniel; Slovic, Paul; and Tversky, Amos, eds. Judgment Under Uncertainty: Heuristics and Biases New York, NY: Cambridge University Press, 1982.
    • Mosteller, Frederick. Fifty Challenging Problems in Probability with Solutions Mineola, NY: Dover, 1987.
    • Newman, Claire M.; Obremski, Thomas E.; and Scheaffer, Richard L. Exploring Probability Palo Alto, CA: Dale Seymour, 1987.
      • Packel, Edward W. The Mathematics of Games and Gambling Washington, DC: Mathematical Association of America, 1981.

Renyi, Alfred. Letters on Probability Detroit, MI: Wayne State University Press, 1973.

Thorp, Edward O. Beat the Dealer: A Winning Strategy for the Game of Twenty-One New York, NY: Vintage Books, 1966.

Wagenaar, Willem A. Paradoxes of Gambling Behaviour Hillsdale, NJ: Lawrence Erlbaum, 1988.

      • Weaver, Warren. Lady Luck: The Theory of Probability Mineola, NY: Dover, 1982.


Probability: Elementary

Bremaud, Pierre. An Introduction to Probabilistic Modeling New York, NY: Springer-Verlag, 1988.

      • Chung, Kai Lai. Elementary Probability Theory with Stochastic Processes, New York, NY: Springer-Verlag, 1974, 1979. Third Edition.

Cramer, Harald. The Elements of Probability Theory, Melbourne, FL: Robert E. Krieger, 1973. Second Edition.

  • Gnedenko, Boris V. and Khinchin, A. Ya. An Elementary Introduction to the Theory of Probability Mineola, NY: Dover, 1962.

Hodges, Joseph L. and Lehmann, E.L. Elements of Finite Probability, San Francisco, CA: Holden-Day, 1970. Second Edition.

Hoel, Paul G.; Port, Sidney C.; and Stone, Charles J. Introduction to Probability Theory Boston, MA: Houghton Mifflin, 1971.

  • Khazanie, Ramakant. Basic Probability Theory and Applications Santa Monica, CA: Goodyear, 1976.

Mosteller, Frederick, et al. Probability with Statistical Applications, Reading, MA: Addison-Wesley, 1970. Second Edition.

Olkin, Ingram; Gleser, L.J.; and Derman, C. Probability Models and Applications New York, NY: Macmillan, 1978.

Ross, Sheldon M. Introduction to Probability Models, New York, NY: Academic Press, 1972, 1985. Third Edition.

    • Scheaffer, Richard L. Introduction to Probability and Its Applications Boston, MA: PWS-Kent, 1990.
    • Snell, J. Laurie. Introduction to Probability Cambridge, MA: Random House, 1988.
  • Tuckwell, Henry C. Elementary Applications of Probability Theory New York, NY: Chapman and Hall, 1988.


Probability: Advanced

Breiman, Leo. Probability Reading, MA: Addison-Wesley, 1968.

  • Chow, Yuan Shih and Teicher, Henry. Probability Theory: Independence, Interchangeability, Martingales, New York, NY: Springer-Verlag, 1988. Second Edition.
    • Chung, Kai Lai. A Course in Probability Theory, New York, NY: Academic Press, 1974. Second Edition.

Cramer, Harald. Random Variables and Probability Distributions, New York, NY: Cambridge University Press, 1970. Third Edition.

Durrett, Richard. Probability: Theory and Examples Belmont, CA: Wadsworth, 1991.

      • Feller, William. An Introduction to Probability Theory and Its Applications, New York, NY: John Wiley, 1968, 1971. 2 Vols., Second Edition.
  • Gnedenko, Boris V. The Theory of Probability and the Elements of Statistics, New York, NY: Chelsea, 1967, 1989. Fifth Edition.

Hunter, Jeffrey J. Mathematical Techniques of Applied Probability New York, NY: Academic Press, 1983.

Johnson, Norman L. and Kotz, Samuel. Urn Models and Their Application: An Approach to Modern Discrete Probability Theory New York, NY: John Wiley, 1977.

    • Kac, Mark. Statistical Independence in Probability, Analysis, and Number Theory Washington, DC: Mathematical Association of America, 1959.
  • Lloyd, Emlyn. Probability New York, NY: John Wiley, 1980. Handbook of Applicable Mathematics, Volume II.
    • Loeve, Michel M. Probability Theory, New York, NY: Springer-Verlag, 1978. 2 Vols., Fourth Edition.

Moran, Patrick A. An Introduction to Probability Theory New York, NY: Oxford University Press, 1968, 1984.

Parzen, Emanuel. Modern Probability Theory and Its Applications New York, NY: John Wiley, 1960.

Rao, M.M. Probability Theory with Applications New York, NY: Academic Press, 1984.

  • Rosenblatt, Murray, ed. Studies in Probability Theory Washington, DC: Mathematical Association of America, 1978.
      • Rothschild, V. and Logothetis, N. Probability Distributions New York, NY: John Wiley, 1986.

Shiryayev, A.N. Probability New York, NY: Springer-Verlag, 1984.

Spencer, Joel H. Ten Lectures on the Probabilistic Method Philadelphia, PA: Society for Industrial and Applied Mathematics, 1987.

Trivedi, Kishor S. Probability and Statistics with Reliability, Queueing, and Computer Science Applications: John Wiley & Sons, Inc. New York, 2002.

  • Tucker, Howard G. A Graduate Course in Probability New York, NY: Academic Press, 1967.

Stochastic Processes

Bailey, Norman T.J. The Elements of Stochastic Processes with Applications to the Natural Sciences New York, NY: John Wiley, 1990.

  • Bhat, U. Narayan. Elements of Applied Stochastic Processes, New York, NY: John Wiley, 1984. Second Edition.

Brockwell, Peter J. and Davis, Richard A. Time Series: Theory and Methods, New York, NY: Springer-Verlag, 1987, 1991. Second Edition.

Chow, Yuan Shih; Robbins, Herbert; and Siegmund, David. Great Expectations: The Theory of Optimal Stopping Mineola, NY: Dover, 1991.

Chung, Kai Lai and Williams, R.J. Introduction to Stochastic Integration, New York, NY: Birkhauser, 1983, 1990. Second Edition.

Cox, D.R. and Isham, Valerie. Point Processes New York, NY: Chapman and Hall, 1980.

Cox, D.R. and Smith, W.L. Queues New York, NY: Halsted Press, 1961.

Cramer, Harald and Leadbetter, M.R. Stationary and Related Stochastic Processes New York, NY: John Wiley, 1970.

  • Dellacherie, Claude and Meyer, Paul-Andre. Probabilities and Potential Amsterdam: North-Holland, 1978.
      • Doob, J.L. Stochastic Processes New York, NY: John Wiley, 1965, 1990.
  • Doyle, Peter G. and Snell, J. Laurie. Random Walks and Electric Networks Washington, DC: Mathematical Association of America, 1984.

Dubins, Lester E. and Savage, Leonard J. Inequalities for Stochastic Processes (How to Gamble If You Must) Mineola, NY: Dover, 1976.

  • Hida, T. Brownian Motion New York, NY: Springer-Verlag, 1980.
    • Kallinpur, Gopinath. Stochastic Filtering Theory New York, NY: Springer-Verlag, 1980.
  • Karlin, Samuel and Taylor, Howard M. A First Course in Stochastic Processes, New York, NY: Academic Press, 1975. Second Edition.

Karlin, Samuel and Taylor, Howard M. A Second Course in Stochastic Processes New York, NY: Academic Press, 1981.

Kemeny, John G. and Snell, J. Laurie. Finite Markov Chains New York, NY: Springer-Verlag, 1976.

Kemeny, John G.; Snell, J. Laurie; and Knapp, Anthony W. Denumerable Markov Chains, New York, NY: Springer-Verlag, 1976. Second Edition.

Lukacs, Eugene. Stochastic Convergence, New York, NY: Academic Press, 1975. Second Edition.

  • Medhi, J. Stochastic Processes New York, NY: Halsted Press, 1982.
  • Nelson, Edward. Radically Elementary Probability Theory Princeton, NJ: Princeton University Press, 1987.

Port, Sidney C. and Stone, Charles J. Brownian Motion and Classical Potential Theory New York, NY: Academic Press, 1978.

Rosenblatt, Murray. Random Processes, New York, NY: Springer-Verlag, 1974. Second Edition.

    • Ross, Sheldon M. Stochastic Processes New York, NY: John Wiley, 1983.

Skorokhod, A.V. Studies in the Theory of Random Processes Mineola, NY: Dover, 1982.

  • Sobol, I.M. The Monte Carlo Method Moscow: MIR, 1975.

Spitzer, Frank. Principles of Random Walk New York, NY: Van Nostrand Reinhold, 1964.

Syski, R. Random Processes: A First Look, New York, NY: Marcel Dekker, 1979, 1989. Second Edition.

  • Taylor, Howard M. and Karlin, Samuel. An Introduction to Stochastic Modeling New York, NY: Academic Press, 1984.

Tops e, Flemming. Spontaneous Phenomena: A Mathematical Analysis New York, NY: Academic Press, 1990.


Probability: Foundations

Fine, Terrence L. Theories of Probability: An Examination of Foundations New York, NY: Academic Press, 1973.

Good, I.J. Good Thinking: The Foundations of Probability and Its Applications Minneapolis, MN: University of Minnesota Press, 1983.

Harper, W.L. and Hooker, C.A., eds. Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Sciences, Norwell, MA: D. Reidel, 1976. 2 Vols.

    • Kolmogorov, Andrei N. Foundations of the Theory of Probability, New York, NY: Chelsea, 1950, 1956. Second Edition.

Renyi, Alfred. Foundations of Probability San Francisco, CA: Holden-Day, 1970.

  • Shafer, Glenn. A Mathematical Theory of Evidence Princeton, NJ: Princeton University Press, 1976.
  • de Finetti, Bruno. Probability, Induction, and Statistics New York, NY: John Wiley, 1972.
    • de Finetti, Bruno. Theory of Probability: A Critical Introductory Treatment, New York, NY: John Wiley, 1974, 1975. 2 Vols.
      • von Mises, Richard. Probability, Statistics, and Truth, Mineola, NY: Dover, 1981. Second Revised English Edition.


Measure Theory

Ash, Robert B. Real Analysis and Probability New York, NY: Academic Press, 1972.

Bauer, Heinz. Probability Theory and Elements of Measure Theory, New York, NY: Academic Press, 1978, 1981. Second English Edition.

  • Billingsley, Patrick. Convergence of Probability Measures New York, NY: John Wiley, 1968.
    • Billingsley, Patrick. Probability and Measure, New York, NY: John Wiley, 1979, 1986. Second Edition.

Dudley, Richard M. Real Analysis and Probability Belmont, CA: Wadsworth, 1989.

Kallenberg, Olav. Random Measures New York, NY: Academic Press, 1983.

  • Kingman, J.F.C. and Taylor, S.J. Introduction to Measure with Probability New York, NY: Cambridge University Press, 1966.
  • Krieger, Henry A. Measure-theoretic Probability Lanham, MD: University Press of America, 1980.
    • Parthasarathy, K.R. Probability Measures on Metric Spaces New York, NY: Academic Press, 1967.


Probability: Fuzzy Sets

Kaufmann, Arnold and Gupta, Madan M. Introduction to Fuzzy Arithmetic: Theory and Applications New York, NY: Van Nostrand Reinhold, 1985.

  • Kaufmann, Arnold. Introduction to the Theory of Fuzzy Subsets, New York, NY: Academic Press, 1975.

Klir, George J. and Folger, Tina A. Fuzzy Sets, Uncertainty, and Information Englewood Cliffs, NJ: Prentice Hall, 1988.

Yager, R.R. Fuzzy Sets and Possibility Theory Elmsford, NY: Pergamon Press, 1982.


Probability: Special Topics

Bharucha-Reid, A.T. Probabilistic Methods in Applied Mathematics, New York, NY: Academic Press, 1968, 1970. 2 Vols.

Doob, J.L. Classical Potential Theory and Its Probabilistic Counterpart New York, NY: Springer-Verlag, 1984.

    • Gray, Robert M. Probability, Random Processes, and Ergodic Properties New York, NY: Springer-Verlag, 1988.

Grenander, Ulf. Probabilities on Algebraic Structures New York, NY: John Wiley, 1963.

  • Gudder, Stanley P. Quantum Probability New York, NY: Academic Press, 1988.
    • Romano, Joseph P. and Siegel, Andrew F. Counterexamples in Probability and Statistics Belmont, CA: Wadsworth, 1986.
  • Solomon, Herbert. Geometric Probability Philadelphia, PA: Society for Industrial and Applied Mathematics, 1978.

Springer, M.D. The Algebra of Random Variables New York, NY: John Wiley, 1979.

    • Szekely, Gabor J. Paradoxes in Probability Theory and Mathematical Statistics Norwell, MA: D. Reidel, 1986.
  • Yaglom, A.M. and Yaglom, I.M. Probability and Information Norwell, MA: D. Reidel, 1983.



Markov chain

  • A.A. Markov. "Rasprostranenie zakona bol'shih chisel na velichiny, zavisyaschie drug ot druga". Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete, 2-ya seriya, tom 15, pp 135-156, 1906.
  • A.A. Markov. "Extension of the limit theorems of probability theory to a sum of variables connected in a chain". reprinted in Appendix B of: R. Howard. Dynamic Probabilistic Systems, volume 1: Markov Chains. John Wiley and Sons, 1971.
  • Leo Breiman. Probability. Original edition published by Addison-Wesley, 1968; reprinted by Society for Industrial and Applied Mathematics, 1992. ISBN 0-89871-296-3. (See Chapter 7.)
  • J.L. Doob. Stochastic Processes. New York: John Wiley and Sons, 1953. ISBN 0-471-52369-0.
  • Booth, Taylor L., Sequential Machines and Automata Theory, John Wiley and Sons, Inc. 1967,

Extensive, wide-ranging book meant for specialists, written for both theoretical computer scientists as well as electrical engineers. With detailed explanations of state minimization techniques, FSMs, Turing machines, Markov processes, and undecidability. Excellent treatment of Markov processes pp.449ff. Discusses Z-transforms, D transforms in their context.

  • Kemeny, John G., Hazleton Mirkil, J. Laurie Snell, Gerald L. Thompson , Finite Mathematical Structures. Prentice-Hall, Inc., 1959


  • E. Nummelin. "General irreducible Markov chains and non-negative operators". Cambridge University Press, 1984, 2004. ISBN 0-521-60494-X

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