## 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