Intro Stoch Diff Equations

3 Credits · Level: Graduate, Undergraduate

Many real-world systems, from finance to physics to neuroscience, exhibit random behavior that can be modeled using stochastic differential equations (SDEs). This course provides a first introduction to SDEs. After reviewing some essential probability theory, we construct and analyze Brownian motion. We then develop Itô’s integral, including the chain and product rules. Finally, we study Itô SDEs, examining existence and uniqueness of solutions and exploring applications to partial differential equations and option pricing.