Lecture Notes
Probability and Stochastic Processes
Lecture Notes
Problem Sets
References and Further Reading
Click on linked topics to view lecture notes.
What is a Stochastic Differential Equation?
Itô’s Formula
Probability Measure
Distribution Functions
Independence
Markov Processes: The Poisson Process
The Poisson Process: Use of Generating Functions
Click on the following links topics for problems.
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, 2000Sheldon 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, 2004Steven 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