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* Title: 'An Introduction to Stochastic Differential Equations
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* Instructor: Xiaohui Xie
* Meeting information:
Regular lecture: TT 3:00-4:20
* Meeting place: ICS 213
Prerequisites
* multivariate calculus, linear algebra, elementary differential equations (at the level of Math 3D at UCI), and (helpful to know) some elementary probability
Course Description
Tentative topics:
* Markov Chains and Linear Difference Equations
* Continuous Time Markov Processes
* Poisson Counters and Differential Equations
* Wiener Processes and Differential Equations
* Ito's calculus and Ito Formula
* Diffusion, Fokker-Planck Equations
* Probability space, Foundation of stochastic processes
* Conditional Expectation, Martingales
* Markov Properties, Feymann-Kac Theorem, Kolmogorov backward equation
* Application to stochastic control
* Application to filtering problems
* Application to population genetics
Lecture notes
Textbook
* Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal
Homework
Exam
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