Stochastic Differential Equations

This lecture covers the theory of Stochastic Differential Equations (SDEs), focusing on finding solutions to equations involving functions f(x) and g(x). It discusses the conditions for the existence and uniqueness of solutions, emphasizing Lipschitz and linear growth properties. The lecture also explores the application of SDEs in various examples, highlighting the challenges in finding explicit solutions. Additionally, it delves into the properties of locally Lipschitz and linearly growing functions, providing insights into the uniqueness and existence of solutions for SDEs.