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| - | ===== Course information ===== | + | ==== Math 227C / CS 285: An Introduction to Stochastic Differential Equations ==== |
| - | * * Title: '''An Introduction to Stochastic Differential Equations''' | + | |
| - | * * 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 ===== | + | == Course information == |
| - | Tentative topics: | + | * Instructor: Xiaohui Xie |
| - | * * Markov Chains and Linear Difference Equations | + | * Meeting information: |
| - | * * Continuous Time Markov Processes | + | * Regular lecture: TT 3:00-4:20 |
| - | * * Poisson Counters and Differential Equations | + | * Meeting place: ICS 213 |
| - | * * 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 ===== | + | == Prerequisites == |
| - | * | + | * multivariate calculus, linear algebra, elementary differential equations (at the level of Math 3D at UCI), and (helpful to know) some elementary probability |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/CourseScribeNotes.pdf Combined scribe notes] | + | |
| - | * | + | == Course Description == |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture1.pdf Lecture 1] | + | Tentative topics: |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture2.pdf Lecture 2] | + | * Markov Chains and Linear Difference Equations |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture3.pdf Lecture 3] | + | * Continuous Time Markov Processes |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture4.pdf Lecture 4] | + | * Poisson Counters and Differential Equations |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture7.pdf Lecture 7] | + | * Wiener Processes and Differential Equations |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture9.pdf Lecture 9] | + | * Ito's calculus and Ito Formula |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture10.pdf Lecture 10] | + | * Diffusion, Fokker-Planck Equations |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture11.pdf Lecture 11] | + | * Probability space, Foundation of stochastic processes |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture12.pdf Lecture 12] | + | * Conditional Expectation, Martingales |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture13.pdf Lecture 13] | + | * Markov Properties, Feymann-Kac Theorem, Kolmogorov backward equation |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture14.pdf Lecture 14] | + | * Application to stochastic control |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture17.pdf Lecture 17] | + | * Application to filtering problems |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture18.pdf Lecture 18] | + | * Application to population genetics |
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture19.pdf Lecture 19] | + | |
| - | ===== Textbook ===== | + | == Lecture notes == |
| - | * Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal | + | * [http://www.ics.uci.edu/~xhx/courses/math227c/CourseScribeNotes.pdf Combined scribe notes] |
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture1.pdf Lecture 1] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture2.pdf Lecture 2] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture3.pdf Lecture 3] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture4.pdf Lecture 4] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture7.pdf Lecture 7] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture9.pdf Lecture 9] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture10.pdf Lecture 10] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture11.pdf Lecture 11] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture12.pdf Lecture 12] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture13.pdf Lecture 13] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture14.pdf Lecture 14] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture17.pdf Lecture 17] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture18.pdf Lecture 18] | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture19.pdf Lecture 19] | ||
| + | == Textbook == | ||
| + | * Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal | ||
| - | ===== Homework ===== | ||
| - | * * [https://eee.uci.edu/14s/35340/home/ps1.pdf Assignment #1] Due date: 04/17 (Thur) before class. | ||
| - | * * [https://eee.uci.edu/14s/35340/home/ps2.pdf Assignment #2] Due date: 05/01 (Thur) before class. | ||
| - | * * [http://www.ics.uci.edu/~xhx/courses/math227c/ps3.pdf Assignment #3] Due date: 05/15 (Thur) before class. | ||
| - | * * [https://eee.uci.edu/14s/35340/home/ps4.pdf Assignment #4] Due date: 05/29 (Thur) before class. | ||
| - | ===== Exam ===== | + | == Homework == |
| - | * [https://eee.uci.edu/14s/35340/home/final14.pdf Final Exam] Due date: 06/10 (Tues) before 5pm. | + | * [https://eee.uci.edu/14s/35340/home/ps1.pdf Assignment #1] Due date: 04/17 (Thur) before class. |
| + | * [https://eee.uci.edu/14s/35340/home/ps2.pdf Assignment #2] Due date: 05/01 (Thur) before class. | ||
| + | * [http://www.ics.uci.edu/~xhx/courses/math227c/ps3.pdf Assignment #3] Due date: 05/15 (Thur) before class. | ||
| + | * [https://eee.uci.edu/14s/35340/home/ps4.pdf Assignment #4] Due date: 05/29 (Thur) before class. | ||
| - | ===== [[scribeinfo | Preparing scribe notes]] ===== | + | == Exam == |
| + | * [https://eee.uci.edu/14s/35340/home/final14.pdf Final Exam] Due date: 06/10 (Tues) before 5pm. | ||
| - | * [[Math 227C scribe notes signup]] | ||