Understanding Brownian Motion, Martingales, and Stochastic Calculus

Understanding Brownian Motion, Martingales, and Stochastic Calculus provides a concise and rigorous introduction to the theory of stochastic calculus for continuous semimartingales, with a special emphasis on Brownian motion.

The book covers a wide range of topics, including:

Brownian motion and its properties
Martingales and their basic properties
Stochastic integration and Itô’s formula
Markov processes and harmonic functions

Stochastic differential equations and their applications to quantitative finance

The book is written in a clear and concise style, and it includes a number of exercises to help the reader solidify their understanding of the material. It is an excellent choice for students and researchers who are interested in learning about the theory and applications of stochastic calculus.