Lecture Notes

Probability and Stochastic Processes

  • Lecture Notes

  • Click on linked topics to view lecture notes.

    What is a Stochastic Differential Equation?
    Itô’s Formula
    Probability Measure
    Distribution Functions
    Independence

  • Problem Sets

  • Click on the following links topics for problems.

  • References and Further Reading

  • Normal T. J. Bailey, The elements of Stochastic Processes with applications to the natural sciences, John Wiley & Sons, Inc., 1964
    S. Chandrasekhar, Stochastic Problems in Physics and Astronomy, Reviews of Modern Physics, Volume 15, Number 1, January, 1943, 1-89
    Lawrence C. Evans, An Introduction to Stochastic Differential Equations, Lecture Notes
    Extended version of the lecture notes has been published as a book.
    Lawrence C. Evans, An Introduction to Stochastic Differential Equations, American Mathematical Society, 2014
    Jan A Freund, Thorsten Pöschel (Eds.), Stochastic Processes in Physics, Chemistry, and Biology, Springer, 2000
    Robert M. Gray, Probability, Random Processes, and Ergodic Properties, Spinger Verlag, 1987
    Robert V. Hogg, Allen T. Craig, Introduction to Mathematical Statistics, Fourth Edition, Macmillan Publishing Co.. Inc., 1978
    D. Kannan, An Introduction to Stochastic Proceses, North Holland, 1979
    Don S. Lemons, An Introduction to Stochastic Processes in Physics, The Johns Hopkins University Press, 2002

    Containing "On the Theory of Brownian Motion" by Paul Langevin, translated by Anthony Gythiel

    Bernt Øksendal, Stochastic Differential Equations, An Introduction with Applications, 5th Edition, Springer, 2000
    Sheldon Ross, A First Course in Probability, Fifth Edition, Prentice Hall, 1997
    Steven E. Shreve, Stochastic Calculus and Finance, Lecture Notes

    Extended version of Steven Shreve's lecture notes has been published as two books.

    Steven E. Shreve, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer, 2004
    Steven E. Shreve, Stochastic Calculus for Finance II: Continuous Time Models, Springer, 2004
    L. Takács, Stochastic Processes, Problems and Solutions, John Wiley & Sons Inc., 1960
    Jan Vrbik, Paul Vrbik, Informal Introduction to Stochastic Processes with Maple, SPringer, 2013