Stochastic Integration and Differential Equations

The book "Stochastic Integration and Differential Equations" offers a comprehensive and well-founded introduction to stochastic integration and differential equations. The second edition, published 15 years after the first edition, includes significant updates and additions. Notably, it features the introduction of exercises designed to help readers deepen their understanding of the concepts. These exercises were developed in collaboration with students from renowned universities and are intended to apply theoretical knowledge practically. The revision of the third chapter provides an intuitive and accessible approach to key theorems, while the fourth chapter addresses sigma-martingales, which are important in financial theory. The modern treatment of compensators and the comprehensive presentation of the martingale representation make this work a valuable resource for students and professionals in the fields of mathematics and finance.