This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

**Key topics include**:

* Markov processes

* Stochastic differential equations

* Arbitrage-free markets and financial derivatives

* Insurance risk

* Population dynamics, and epidemics

* Agent-based models

**New to the Third Edition**:

* Infinitely divisible distributions

* Random measures

* Levy processes

* Fractional Brownian motion

* Ergodic theory

* Karhunen-Loeve expansion

* Additional applications

* Additional exercises

* Smoluchowski approximation of Langevin systems

*An Introduction to Continuous-Time Stochastic Processes, Third Edition* will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided.

From reviews of previous editions:

*"The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications."* —**Zentralblatt MATH**