This site lists free online lecture notes and books on stochastic processes and applied probability, stochastic calculus, measure theoretic probability, probability distributions, Brownian motion, financial mathematics, Markov Chain Monte Carlo, martingales.
If you know of any additional appropriate book or course notes that are available on line, please send an e-mail to the address below.
Contact: Myron Hlynka at
Last update: February 15, 2014.
The books/lecture notes below are in alphabetical order, by author.





  1. Virtual Laboratories in Probability and Statistics. University of Alabama - Huntsville.
    I really like this site. Take a look. There is a wealth of information here. Congratulations to those who prepared this site. Brilliant.
  2. Patrik ALBIN. 2010. MSF200/MVE330 Stochastic Processes. Goteborg, Sweden. 74 pp.
  3. David ALDOUS and James FILL. 1999. Reversible Markov Chains and Random Walks on Graphs
  4. William ANDERSON, 2005. Notes for Elementary Stochastic Proceesses, McGill University. 70 pp.
  5. Robert B. ASH. 2008. Basic Probability Theory
  6. Lothar BREUER. 2007. Introduction to Stochastic Processes. 84 pp.
  7. Wlodzimierz BRYC. 1995. Applied Probability and Stochastic Processes. Lecture Notes for 577/578 Class, University of Cincinnati
  8. Jiahua CHEN. 2003. Stat 333 Lecture Notes. Applied Probability Theory. University of Waterloo.
    1.Intro. 2. Random Variables. 3. Conditional Expectation. 4 Generating Functions; 5 Renewal Events; 6 Discrete Time MC; 7 Exponential and Poisson; 8 Continuous Time Markov Chain; 9 Queueing Theory; 10 Renewal Process. 172 pp.
  9. Ke-Sheng CHENG. 2006. Random Processes. National Taiwan University.
  10. Randy COGHILL. 2010. Sys 6005 course notes. U of Virginia. Markov chains, Applications (Google page rank, MCMC models), hidden Markov models, continuous Markov processes
  11. Luc DEVROYE. 1986. Non Uniform Random Variate Generation, Springer Verlag. Over 600 pp.
  12. Marco A.G. DIAS. "Stochastic Processes with Focus in Petroleum Applications"
    Brownian motion, Ito's lemma, ...
  13. Bruce K. DRIVER. 2008. Math 180C (Introduction to Probability) Notes. U. of California, San Diego.
  14. Muhammed EL-TAHA. 2007. Stochastic Modeling in Operations Research, by (University of Southern Maine)(classnotes)
    Markov chains, Poisson processes, queueing, reliability.
  15. Renato FERES. Washington University. St. Louis. Math 450 - Topics in Applied Mathematics. Random Processes. 2007
  16. SC: Rachel FEWSTER. STATS 325. University of Auckland.
  17. P. A. FERRARI, A. GALVES. 2001. Coupling and regeneration for stochastic processes. pdf Corrected version, 153 + 12 pages
    Also, different,
  19. Christopher GENOVESE. 2006. 36-703 INTERMEDIATE PROBABILITY. Carnegie Mellon University.
  20. Janko GRAVNER. 2011. Lecture Notes for Introductory Probability University of California, Davis. Markov chains start in Chapter 15.
  21. Robert M. GRAY. Probability, Random Processes, and Ergodic Properties. Stanford University. 2008.
  22. Charles GRINSTEAD and J. Laurie SNELL. Introduction to Probability.
    Chapter 10 Branching processes. Chapter 11 Markov chains.
  23. Bruce HAJEK. Notes for ECE 534.
    An Exploration of Random Processes for Engineers
    July, 2006.
  24. Zhenting HOU, Qingfeng GUO. 1988. Homogeneous Denumerable Markov Processes, Springer-Verlag, Germany, Science Press, Beijing, 282 pages
  25. Olle HAGGSTROM. Lecture Notes on Markov Chains. 2004. 78 pp.
  26. Magdalena HYSKOVA. Stochastic Models. Click on "Study Materials"
  27. Kiyoshi IGUSA. 2008. Notes for course Math 56a. Brandeis University. Markov chains.
  28. Ed IONIDES. 2009. Stat 620. Applied Probability and Stochastic Modeling. University of Michigan.
  29. Valerie ISHAM. 2009. LTCC Course on Stochastic Processes. University College London.
    Discrete Markov chains, Continuous time Markov chains. reversibility, point processes, epidemic models. 64 pp.
  30. JACOBSEN, KEIDING, MARTINUSSEN, NIELSEN, MADSEN, NIELSEN, BRIX. 2007. Problems in Markov chains. 34 pp.
  31. Frank P. KELLEY. 1979. Reversibility and Stochastic Networks. A classic text. 235 pp.
  32. KINDERMAN AND SNELL. 1980. Markov Random Fields and their Applications, 147 pp. American Mathematical Society Press.
  33. Takis KONSTANTOPOULOS. 2009. Markov Chains and Random Walks. 128 pp.
  34. Ger KOOLE. Lecture notes "Optimization of business processes." November 2007. 237 pp.
  35. Peter KRAMER. 2010. Introduction to Stochastic Processes. MATH 6790-1, Rennsaeller Polytechnical Institute.
  36. Steve LALLEY. 2007. Course Notes for Stat 313: Stochastic Processes. MCMC. Continuous time MC, martingales, Wiener processes. U. of Chicago.
  37. Neil LAWS. Applied Probability. 2010.
  38. Georg LINDGREN. 1999. Lund University. Lectures on Stationary Stochastic Processes; a course for PhD students in mathematical statistics and other fields Lund, May 1999
  39. Marco LIPPI. 2006. Discrete-Time Stationary Stochastic Processes Lecture Notes. (Measure Theory, time series) University of Rome.
    The spectral representation of wide sense stationary processes, Linear filtering, Linear prediction and the Wold representation, Obtaining the Wold representation from the spectral density.
  40. Nelly LITVAK and Werner SCHEINHARDT. 2009. Introduction to stochastic processes. Univ. of Twente.
  41. Robert LIPSTER. Department of Electrical Engineering-Systems , Tel Aviv University. Lecture notes on ``Stochastic Processes'' and on ``Stochastic Control''
  42. Ira M. LONGINI, JR., Michael G. HUDGENS. 2003. Lecture Notes on Stochastic Processes in Biostatistics.
  43. John LUI. Computer System Performance Evaluation (CSC5420). 2009. Hong Kong.
  44. Russell LYONS. Indiana University. Stochastic Processes. 104 pp.
  45. Ravi MAZUMDAR. 2009. ECE604. Stochastic Processes. University of Waterloo.
  46. Sean MEYN & Richard TWEEDIE, Markov Chains and Stochastic Stability, Springer, 1996
    Winner of the 1994 ORSA/TIMS Award for the best research publication in Applied Probability. 536 pages.
  48. Peter MORTERS. 1999-2000. Lecture Notes in Probability, Universitat Kaiserslautern.
  49. Peter MORTERS. 2000. Lecture Notes in Stochastic Processes, Universitat Kaiserslautern. Martingales. Stochastic Integrals. Stochastic Calculus. Brownian Motion.
  50. Phillipe NAIN. Stochastic Processes Lecture Notes.
  51. Soren Nielsen. Continuous-time homogeneous Markov chains. 32 pp.
  52. James NORRIS. Part of the book "Markov Chains" by J. R. Norris, University of Cambridge
  53. David NUALART. Stochastic Processes. University of Barcelona. 148 pp.
  54. Pekka ORPONEN. 2003. T-79.250 Combinatorial Models and Stochastic Algorithms Spring 2003. Helsinki University of Technology.
  55. Tony PAKES. 2010. STAT3361 RANDOM PROCESSES & THEIR APPLICATIONS. University of Western Australia.
  56. Jim PITMAN. 2010. Statistics 150: Stochastic Processes. U.C. Berkeley.
  57. Andreas RASMUSSON. A Collection of Links to Computer Science Resources, including probability and stochastic processes. Nothing on queueing that I could see, but a wonderful collection nevertheless. This site comes from Andreas Rasmusson in the Swedish Insititute of Computer Science.
  58. Bruce REED. 2008. 308-760B Applied Stochastic Processes. McGill University.
  59. Simon RUBINSTEIN-SALZEDO. 2005. Probability Theory and Stochastic Processes. Notes from PStat 213A with Professor Raya Feldman. University of Albany.
  60. Marek RUTKOWSKI. STAT3011/3911: STOCHASTIC PROCESSES. University of Sydney. 2011.
  61. M. SCOTT. 2013. Applied Stochastic Processes in science and engineering. 309 pp. Brownian Motion. Random Processes. Markov Processes. Master Equation. Perturbation. Fokker-Planck. Stochastic Calculus. Random Differential Equations.
  62. E. SENETA and M.S. PEIRIS. 2011. STAT 3011 Stochastic Processes and Time Series. University of Sydney.
  63. Mehrdad SHAHSHAHANI. (Iran) Introduction to stochastic processes,
  64. Volker SCHMIDT. 2006. Markov Chains and Monte-Carlo Simulation. Lecture Notes. University Ulm, Department of Stochastics.
  65. Stochastic Processes, Web course, NPTEL Phase II (with Prof. N. Selvaraju)
  66. Karl SIGMAN. Stochastic Modeling Course. Lecture Notes, Columbia University, New York, 2001.
  67. Karl SIGMAN. Stochastic Models II (IEOR 6712) notes, by 2005. Columbia University.
  68. John STENSBY. Course Notes for "Random Signals and Noise." Essentially a book in advanced probability.
  69. Yuri SUHOV. Part II APPLIED PROBABILITY. Cambridge. 2011
  70. Modeling and Analysis of Information Technology Systems. by Dr. János Sztrik. University of Debrecen, Faculty of Informatics. 2011. Nice online book. 115 pp.
  71. Glen TAKAHARA. 2010. STAT 455/855 course notes. Queen's University. Kingston, Ontario.
  72. Fabrice VALOIS. 2006. Introduction to Markov Chains and Queueing Theory, Lecture Notes. (in French)
    1. Part 1
    2. Part 2
    3. Part 3
    4. Part 4
    5. Part 5
  73. Ramon VAN HANDEL. 2008. Hidden Markov Models Lecture Notes.
  74. Harry VAN ZANTEN. 2004. An Introduction to Stochastic Processes in Continuous Time.
  75. S.R.Srinivasa VARADHAN. 2011. Stochastic Processes Notes. Courant Institute of Mathematical Sciences New York University
  76. Jan VRBIK. Lecture Notes for Stochastic Processes Course. (117 pp.)
  77. J. VRBIK. Lecture Notes and Old Exams. (for a variety of courses including Stochastic Processes). Brock University.
  78. Anton WAKOLBINGER. Stochastic Processes Notes. University of Frankfurt.
  79. Jean WALRAND. 2004. Lecture Notes on Probability Theory and Random Processes. University of California, Berkeley, CA 94720.
  80. Alexander WENTZELL. MATH 777 Markov Processes 2009, Tulane University.
  81. Ward WHITT. 2009. Lecture Notes for IEOR 4106. Columbia University.
  82. I.F. WILDE. Stochastic Analysis - Notes. (103 pages) These notes are based on lectures given in the Mathematics Department, King's College London.
  83. Matthias WINKEL. 2007. "Applied Probability" Notes. 98 pp.
  84. Serdar YUKSEL. Control of Stochastic Systems. Course Notes. Winter 2011. Queen’s Universit. Kingston, Ontario.
  85. Gordan ZITKOVIC. UNIVERSITY OF TEXAS AT AUSTIN M362M: Introduction to Stochastic Processes


  1. Alan BAIN. "Stochastic Calculus." 95 pp.
  2. Klaus BICHTELER. Stochastic integrations and Stochastic Differential Equations. University of Texas.
  3. Loren COBB. 1998. Stochastic Differential Equations for the Social Sciences. 26 pp.
  4. Jesper CARLSSO, Kyoung-Sook MOON, Anders SZEPESSY, Raul TEMPONE, Georgios ZOURARIS. 2010. Stochastic and Partial Differential Equations with Adapted Numerics, 202 pp.
  6. David Gamarnik, Premal Shah. 15.070 Advanced Stochastic Processes. MIT. 2005.
  7. Jonathon GOODMAN. 2004. Stochastic Calculus Lecture Notes. New York University.
  8. Martin HAUGH. 2010. Introduction to Stochastic Calculus.
  9. Davar Khoshnevisan. Stochastic Calculus. Math 7880-1 Spring 2008. University of Utah
  10. Thomas KURTZ. Math 735 Stochastic Differential Equations notes. Lectures on Stochastic Analysis. U of Wisconsin
  11. Haijun Li. MATH 490/583 (An Introduction to Stochastic Calculus), Fall 2010, Wayne State Univ.
  12. Adam MONOHAN. 1998. Stochastic Differential Equations: A SAD Primer, 9 pp.
  13. David NUALART. "Stochastic Calculus" 89 pp.
  14. P.J.C. SPREIJ. 2011. Stochastic integration. 97 pp.
  15. Ramon VAN HANDEL. 2007. Stochastic Calculus, Filtering, and Stochastic Control. Lecture Notes.
  16. S.R.Srinivasa VARADHAN. 2000. Stochastic Processes Notes. Courant Institute of Mathematical Sciences New York University


  1. Robert M. ANDERSON. Lecture Notes on Measure and Probability Theory. 2002. U. California (Berkeley)
  2. Rodrigo BANUELOS. 2003. Lecture Notes: Measure Theory and Probability. 198 pp.
  3. Richard BASS (U of Connecticut) Probability Notes. 2001
    For other lecture notes on measure theory, stochastic calculus, financial mathematics, undergraduate probability, by Richard Bass, go to
  4. Richard BASS. 2008. Stochastic Processes Notes. U of Connecticut. Measure theoretic.
    For other lecture notes on probability, measure theory, stochastic calculus, financial mathematics, undergraduate probability, by Richard Bass, go to
  5. Dimitri P. BERTSEKAS and Steven E. SHREVE. 1978. Stochastic Optimal Control: The Discrete-Time Case, by Academic Press 1978. Republished by Athena Scientific, 1996. Discusses finite and infinite horizon models. Measure theoretic.
  6. Herman J. BIERENS. 2003. Probability and Measure. Pennsylvania State University
  7. Michael Bishop. 2010. Measure and Probability.
  8. Stefano BONACCORSI and Enrico PRIOLA. 2006. Brownian Motion and Stochastic Differential Equations
  9. Amir DENBO. 2008. Stochastic Processes (MATH136, Stanford). , Measure theoretic. 131 pp.
  10. Bruce K. DRIVER. 2007. Math 280 (Probability Theory) Lecture Notes. 233 pp.
  11. Alexander GRIGORYAN. 2008. Measure theory and probability. Lecture notes. 122 pp.
  12. HOU Zhenting, GUO Qingfeng. 1988. Homogeneous Denumerable Markov Processes, Springer-Verlag, Germany, Science Press, Beijing, 282 pages. (measure theoretic)
  13. Davar Khoshnevisan. Math 6040. The University of Utah. Mathematical Probability
  14. Oliver KNILL. 2006. Probability. Caltech. (Measure theoretic) 377 pp.
  15. Vladimir Semenovich Koroliuk, Nikolaos Limnios. Chapter 1 of Stochastic systems in merging phase space.
  16. Michael KOZDRON. Probability. (based on J. Rosenthal's A First Look at Rigorous Probability Theory)
  17. Thomas G. KURTZ. 2000. LMS/EPSRC Short Course on Stochastic Analysis. Oxford University.
  18. Greg LAWLER. Probability Notes. U. of Chicago.
  19. Gregory MIERMONT. Advanced Probability. Part III of the Mathematical Tripos. 2006 92 pp.
  20. Peter MORTERS. 1999-2000. Lecture Notes in Probability, Universitat Kaiserslautern.
  21. Peter MORTERS. 2000. Lecture Notes in Stochastic Processes, Universitat Kaiserslautern. Martingales. Stochastic Integrals. Stochastic Calculus. Brownian Motion.
  22. Efe A. OK (New York University). Probability Theory with Economic Applications.
  23. Yuval PERES. 2002. Statistics 205B : Probability Theory II notes. Berkeley.
  24. Jorn SASS. 2010. Probability Theory I.
  25. M. SCHWEIZER. Stochastic Processes and Stochastic Analysis. 2007. 75 pp.
  26. Timo SEPPALAINEN. Basics of Stochastic Analysis. 2010
    Measure theory, Filtrations and stopping times, Markov property, Brownian motion, Poisson processes, Martingales, Stochastic Integral, Itoˆ'’s forlmua, Stochastic Differential Equations
  27. Cosma SHALIZI with Aryeh Kontorovich. 2010. 36-754, Advanced Probability II
    Almost None of the Theory of Stochastic Processes. 320 pp.
  28. Terence TAO. 254A, Notes 0: A review of probability theory. 2010.
  29. Noel VAILLANT. Probability Tutorials. More measure theory than probability, but all with probability in mind. Very interesting site.
  30. I.F. WILDE. Measure, integration & probability. King's College, London.
  31. Virtual Laboratories in Probability and Statistics.
  32. Youtube Video.
    Measure Theory for Probability Primer: by mathematicalmonk.
  33. Youtube video. Chris Evans. Why use measure theory for probability? 3 parts
    Part 1
    Part 2
    Part 3


  1. Michael P. MCLAUGHLIN. Compendium of Distributions.
  2. Continuous Distributions.
  3. Engineering Statistics Handbook
    NIST/SEMATECH e-Handbook of Statistical Methods
    Contains distributions in Chapter 1 (Explore)


  1. Amir DEMBO. Lecture Notes on Stochastic Processes including a chapter on Brownian Motion
  2. Lawrence EVANS. Lecture notes on Stochastic Differential Equations
  3. Steve LALLEY. Lecture Notes on mathematical finance
  4. Feng YU. Lecture notes on Brownian Motion
  5. Wikipedia article on Brownian Motion.
  6. A Java applet simulating Brownian Motion.


  1. Scot ADAMS and Fernando REITICH. Notes on Financial Mathematics
  2. Stefan ANKIRCHNER. Option Pricing and Financial Mathemtics.
  3. Marco AVELLANEDA. 1996. Topics in Probability: The mathematics of financial risk-management. Courant Institute of Mathematical Sciences
  4. Richard F. BASS. 2003. The Basics of Financial Mathematics. 106 pp.
  5. Michael KOZDRAN. Stochastic Calculus with Applications to Finance 2009
  6. Holger KRAFT. 2005. Lecture Notes. “FINANCIAL MATHEMATICS I: Stochastic Calculus, Option Pricing, Portfolio Optimization. ” University of Kaiserslautern.
  7. Harald LANG. Lectures on Financial Mathematics
  8. Vasily NEKRASOV. Yet another, yet very reader-friendly, introduction to measure theory (for financial mathematics).
  9. M. NEWBY and P.P. MARTIN Mathematics for Finance: Mathematical Processes for Finance, 2005. by
  10. Karl SIGMAN. Notes on Financial Engineering.
  11. E. TICK. Financial Engineering Course Notes.
  12. Fabio TROJANI. Introduction to Probability Theory and Stochastic Processes for Finance. Lecture Notes. 98 pp.
  13. A.W. VAN DER VAART (Vrije U). Martingales, Diffusions, and Financial Mathematics


  1. Persi DIACONIS. The Markov Chain Monte Carlo Revolution
  2. Charles J. GEYER. 2005. Markov Chain Monte Carlo Lecture Notes. 162 pp.
  3. Antonietta MIRA. Introduction to Monte Carlo and MCMC Methods.
  4. R.M. NEAL. 1993. Probabilistic Inference Using Markov Chain Monte Carlo Methods, Technical Report CRG-TR-93-1. 144 pp.
  5. ZHU, DELLEART and TU. Markov Chain Monte Carlo for Computer Vision --- A tutorial.

  1. Prakash BALACHANDRAN. 2008. Fundamental Inequalities, Convergence and the Optional Stopping Theorem for Continuous-Time Martingales. 13 pp.
  2. Michael KOZDRON. Martingales. 5 pp.
  3. Steve LALLEY. Martingale Lectures. 15 pp.
  4. Kevin ROSS. Optional Stopping.
  5. Karl SIGMAN. Introduction to Martingales in discrete time. 8 pp.
  6. Alistair SINCLAIR. Martingales and the Optional Stopping Theorem. 6 pp.
  7. A.W. VAN DER VAART (Vrije U). Martingales, Diffusions, and Financial Mathematics
  8. John B. WALSH. Notes on Elementary Martingale Theory. 44 pp.
  9. Hans Gerber lectures on martingale theory. Video.
  10. Stochastic Processes in Continuous Time. Notes. U of Arizona. Joseph C. Watkins. 2007

Acknowledgements: Dr. Hlynka recognizes funding from the University of Windsor which assists in his research. View Dr. Hlynka's home page at