MAT 425E - Stochastic Ordinary Diff. Eqts

Course Objectives

1. To give basic knowledge of stochastic differential equations
2. Use stochastic differential equations for financial modeling, guided by some problems in applications.

Course Description

Probability space and axioms, random variables, central limit theorem, stochastic processes, Wiener processes (Brownian motion), Ito integrals, ito derivative theorem, existence and uniqueness theorem, weak and strong solutions, solution methods (integrating factor, variation of parameters, first integrals, transformations, etc.) of linear and nonlinear stochastic ordinary differential equations, numerical methods, Feynman-Kac theorem, Girsanov theorem, Fokker-Planck equation and Pawula theorem, Filter problem.