Modeling and Simulation in Science, Engineering and Technology/An Introduction to Continuous-Time Stochastic Processes
(英文，可编辑的pdf电子文档)

Textbook:An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine，Fourth Edition
Author(s): Vincenzo Capasso,David Bakstein

Course Description:
This course 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, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.
Beginning with the fundamentals of probability, it goes on to introduce the theory of stochastic processes, the IIntegral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the course is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations.