## Lecture Notes

### Stochastic Calculus

The intended purpose of these lecture notes is to provide beginners a quick crash course on basic ideas, compuational techniques, and applications of stochastic calculus and stochastic differential equations so readers can advance more easily by filling in gaps with more in-depth knowledge from currently existing so many wonderful books on stochastic calculus and stochastic differential equations.

These lecture notes should be accessible by undergraduate students of mathematics who have taken differential equations and probability. We will also touch applications of stochastic calculus and stochastic differential equations in finance.

#### Lecture Notes

#### Homework

#### 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

Click on the following links topics for homework.

Not in particular order. There are so many wonderful books on Functions of a Complex Variable. I have listed below only some of those books on Functions of a Complex Variable that I am familiar with.

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

Bernt Øksendal, Stochastic Differential Equations, An Introduction with Applications, 5th Edition, Springer, 2000

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