✎ teaching:cs285s14:start

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<h2>Course information</h2>
<div class="level2">
<ul>
<li class="level1"> * Title: <code>'An Introduction to Stochastic Differential Equations</code>' </li>
<li class="level1"> * Instructor:  Xiaohui Xie</li>
<li class="level1"> * Meeting information: </li>
<li class="level1"> <b> Regular lecture: TT 3:00-4:20
  * </b> Meeting place: ICS 213</li>
<li class="level1"> </li>
</ul>

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<h2>Prerequisites</h2>
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<p>
* multivariate calculus, linear algebra, elementary differential equations (at the level of Math 3D at UCI), and (helpful to know) some elementary probability
</p>

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<h2>Course Description</h2>
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<p>
Tentative topics:
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<ul>
<li class="level1"> * Markov Chains and Linear Difference Equations</li>
<li class="level1"> * Continuous Time Markov Processes</li>
<li class="level1"> * Poisson Counters and Differential Equations</li>
<li class="level1"> * Wiener Processes and Differential Equations</li>
<li class="level1"> * Ito's calculus and Ito Formula</li>
<li class="level1"> * Diffusion, Fokker-Planck Equations</li>
<li class="level1"> * Probability space, Foundation of stochastic processes</li>
<li class="level1"> * Conditional Expectation, Martingales</li>
<li class="level1"> * Markov Properties, Feymann-Kac Theorem, Kolmogorov backward equation</li>
<li class="level1"> * Application to stochastic control</li>
<li class="level1"> * Application to filtering problems</li>
<li class="level1"> * Application to population genetics</li>
</ul>

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<h2>Lecture notes</h2>
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<ul>
<li class="level1"> </li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/CourseScribeNotes.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/CourseScribeNotes.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/CourseScribeNotes.pdf</a> Combined scribe notes]</li>
<li class="level1"> </li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture1.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture1.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture1.pdf</a> Lecture 1]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture2.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture2.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture2.pdf</a> Lecture 2]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture3.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture3.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture3.pdf</a> Lecture 3]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture4.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture4.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture4.pdf</a> Lecture 4]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture7.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture7.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture7.pdf</a> Lecture 7]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture9.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture9.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture9.pdf</a> Lecture 9]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture10.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture10.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture10.pdf</a> Lecture 10]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture11.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture11.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture11.pdf</a> Lecture 11]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture12.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture12.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture12.pdf</a> Lecture 12]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture13.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture13.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture13.pdf</a> Lecture 13]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture14.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture14.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture14.pdf</a> Lecture 14]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture17.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture17.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture17.pdf</a> Lecture 17]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture18.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture18.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture18.pdf</a> Lecture 18]</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/lecture19.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/lecture19.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/lecture19.pdf</a> Lecture 19]</li>
</ul>

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<h2>Textbook</h2>
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<p>
* Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal
</p>

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<h2>Homework</h2>
<div class="level2">
<ul>
<li class="level1"> * [<a href="https://eee.uci.edu/14s/35340/home/ps1.pdf" class="urlextern" title="https://eee.uci.edu/14s/35340/home/ps1.pdf" rel="nofollow">https://eee.uci.edu/14s/35340/home/ps1.pdf</a> Assignment #1]  Due date: 04/17 (Thur) before class.</li>
<li class="level1"> * [<a href="https://eee.uci.edu/14s/35340/home/ps2.pdf" class="urlextern" title="https://eee.uci.edu/14s/35340/home/ps2.pdf" rel="nofollow">https://eee.uci.edu/14s/35340/home/ps2.pdf</a> Assignment #2]  Due date: 05/01 (Thur) before class.</li>
<li class="level1"> * [<a href="http://www.ics.uci.edu/~xhx/courses/math227c/ps3.pdf" class="urlextern" title="http://www.ics.uci.edu/~xhx/courses/math227c/ps3.pdf" rel="nofollow">http://www.ics.uci.edu/~xhx/courses/math227c/ps3.pdf</a> Assignment #3]  Due date: 05/15 (Thur) before class.</li>
<li class="level1"> * [<a href="https://eee.uci.edu/14s/35340/home/ps4.pdf" class="urlextern" title="https://eee.uci.edu/14s/35340/home/ps4.pdf" rel="nofollow">https://eee.uci.edu/14s/35340/home/ps4.pdf</a> Assignment #4]  Due date: 05/29 (Thur) before class.</li>
</ul>

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<h2>Exam</h2>
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* [<a href="https://eee.uci.edu/14s/35340/home/final14.pdf" class="urlextern" title="https://eee.uci.edu/14s/35340/home/final14.pdf" rel="nofollow">https://eee.uci.edu/14s/35340/home/final14.pdf</a> Final Exam] Due date: 06/10 (Tues) before 5pm.
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<h2>[[scribeinfo | Preparing scribe notes]]</h2>
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* <a href="/doku.php?id=teaching:cs285s14:math_227c_scribe_notes_signup" class="wikilink2" title="teaching:cs285s14:math_227c_scribe_notes_signup" rel="nofollow">Math 227C scribe notes signup</a>
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