Stochastic Differential Equations for Science and Engineering

Uffe Høgsbro Thygesen received his Ph.D. degree from the Technical University of Denmark in 1999, based on a thesis on stochastic control theory. He worked with applications to marine ecology and fisheries until 2017, where he joined the Department of Applied Mathematics and Computer Science at the same university. His research interests are centered on deterministic and stochastic dynamic systems and involve times series analysis, control, and dynamic games, primarily with applications in life science. In his spare time he teaches sailing and kayaking and learns guitar and photography.

Introduction. Section I. Fundamentals. 2. Diffusive Transport and Random Walks. 3. Stochastic Experiments and Probability Spaces. 4. Brownian Motion. 5. Linear Dynamic Systems. Section II Stochastic Calculus. 6. Stochastic Integrals. 7. The Stochastic Chain Rule. 8. Existence, Uniqueness, And Numerics. 9. The Kolmogorov Equations. Section III. Applications. 10. State Estimation. 11. Expectations to The Future. 12. Stochastic Stability Theory. 13. Dynamic Optimization. 14. Perspectives.