Stochastic Differential Equations

Stochastic growth models offer a practical advantage over purely deterministic ones: they capture both predictable dynamics and random fluctuations in phenomena such as weather patterns, natural disasters, market swings, and disease outbreaks. That blend makes them valuable to anyone whose work depends on how populations expand or shrink. The mathematical preparation for stochastic differential equations, however, is often out of reach for readers without the formal training that mathematics majors receive. This book is written for people who have completed only a few courses in calculus and statistics. It opens with a thorough refresher on the mathematics needed to build and apply stochastic growth models.

The book then turns to population growth models, covering deterministic and stochastic versions of the logistic, generalized logistic, Gompertz, negative exponential, and linear forms. Key terms and concepts are defined precisely, and numerous worked examples are included. Interpretation of results receives more attention than formal theorem and proof, and the focus stays on solution methods for SDEs and how they are applied to stochastic population models. Chapters are included to fill gaps in background knowledge.

The intended readers include advanced undergraduates, beginning graduate students, and professionals in economics, population studies, environmental science, epidemiology, engineering, finance, and the biological sciences who need a gentle route into SDEs. The author, Michael J. Panik, PhD, is a professor in the Department of Economics at the Barney School of Business and Public Administration, University of Hartford, Connecticut. He earned his PhD in economics from Boston College and belongs to the American Mathematical Society, the American Statistical Association, and the Econometric Society.