General Introduction to Stochastic Processes

This course, "General Introduction to Stochastic Processes," provides a comprehensive overview of fundamental concepts and applications in fields such as finance, insurance, and queuing theory. It covers basic notions of continuous time stochastic processes, including continuous time martingales and stopping times, which are essential for optimal decision-making. Students will explore renewal processes that model event timing, as well as the Poisson process, characterized by its memoryless property for modeling random occurrences over fixed intervals. The course explores compound Poisson processes, addressing both the time and size of events pertinent to risk management. Furthermore, it analyzes covariation and quadratic variation, essential for comprehending process fluctuations, and concludes with Itô's formula for jump diffusion processes.