Welcome to the class website for the course Applied Stochastic Analysis. The class will focus on central topics in the calculus of stochastic processes and on related applications in the natural sciences and engineering. For more details see the syllabus and the topics listed below.
Selection of Topics
- Continuous-time Stochastic Processes
- Stochastic Differential Equations
- Ito's Stochastic Calculus
- Ito Integral, Ito Lemma, Ito Isometry
- Dynkin's Formula
- Girsanov Theorem
- Forward and Backward Kolomogorov PDEs
- First Passage Time Problems and Elliptic PDEs
- Numerical Methods for SDEs and SPDEs
- Weak vs Strong Numerical Approximation
- Introduction to Statistical Mechanics
- Langevin Equations, Fluctuation-Dissipation Principle, Boltzmann H-Theorem, Green-Kubo Relations
- Adiabatic elimination of fast degrees of freedom
- Analysis of metastability and rare events
- Applications in physics, biology, and engineering.
For more information see the syllabus Δ.
Grading:
The grade for the class will be based on the homework assignments (see policy below), a midterm exam, and take-home final exam as follows:
Homework Assignments 30%
Midterm Exam (take-home) 30%
Final Exam (take-home) 40%
Homework Policy:
Assignments will be made periodically in the class as appropriate and posted on the website. While it is permissible for you to discuss materials with classmates, the submitted homework must be your own work.
Exams:
The midterm exam will be assigned on Tuesday, October, 30th in class and is due on Tuesday, November, 13th.
The final exam will be assigned on Tuesday, November 27th and is due on Thursday, December 13th.
Supplemental Class Notes:
Class Annoucements:
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