Probability Theory II: Stochastic Calculus

This book offers a modern approach to the theory of continuous-time stochastic processes and stochastic calculus. The content is treated rigorously, comprehensively, and independently. In the first part, the theory of Markov processes and martingales is introduced, with a focus on Brownian motion and the Poisson process. Subsequently, the theory of stochastic integration for continuous semimartingales was developed. A substantial portion is dedicated to stochastic differential equations, th...