ECG795 Stochastic Differential Equations
Fall 2011: 3 credits
Theory of measure, probability, random variables, martingales,
Brownian motion, white noise, Ito's calculus, stochastic
differential equations, applications
3 credits.
Grading |
Tests: 40%; Mid-terms: 30%; Final: 30%;
Guaranteed Grades:
A- ( > 90%); B- ( > 80%); C- ( > 70%);
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Lecture Room |
SEB 1245 |
Lecture Time |
05:30 PM-06:45 PM T-Th |
Office Hours |
Location: SEB3218 Time: 12:00 P.M. to 2:30 P.M. T,Th |
Textbook |
Probability and Measure
3rd Edition
Patrick Billingsley
(Apr 17, 1995)
Stochastic Differential Equations:
Theory and Applications
by L. Arnold
(Dec 15, 2011)
Stochastic Differential Equations
Lawrence C. Evans
UC Berkeley
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Course Calendar
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Date |
Day |
Topics |
Textbook-Sections/Notes |
Aug
29 |
T |
Introduction to SDE
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Th |
Ito's chain rule
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Sep
5 |
T |
Solving SDEs using Ito chain rule
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|
Th |
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Sep
12 |
T |
Measure and Probability
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Th |
Random Variables
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Sep
19 |
T |
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|
Th |
Probability Distribution
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Sep
26 |
T |
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|
Th |
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Oct
3 |
T |
Expectation and Variance
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|
Th |
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Oct
10 |
T |
Distributions, Independence
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|
Th |
Borel-Cantelli lemma, Characteristic fns
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Oct
17 |
T |
Weak and Strong Law of Large Numbers
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Th |
Laplace De-Moivre, Central Limit Thm
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Oct
24 |
T |
Conditional Expectation
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|
Th |
Martingales and Martingale Inequalities
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Oct
31 |
T |
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Th |
Brownian Motion, Random Walks
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Nov
7 |
T |
Levy-Ciesielski Construction
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|
Th |
Sample Path, Cont., Nowhere Diff.
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Nov
14 |
T |
Wiener Integral
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Th |
Ito and Stratonovich Integral
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Nov
21 |
T |
Ito's chain and product rules
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Th |
Thanksgiving
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Nov
28 |
T |
SDE Wellposedness
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Th |
Langevin, Stocks, Ornstein-Uhlenbeck, Brownian Bridge
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Dec
5 |
T |
Stopping Time and Heat PDE
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Th |
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Dec
12 |
T |
Final Exam
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Final Exam
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Th |
Final Exam
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Final Exam
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