Math 667 Stochastic Processes and Probability
Fall 2014

Instructor:
I. H. Dinwoodie, M327 Neuberger Hall (NH)
Office Hours:
Th: 9:00-11:00 A.M.
Fr: 1:00-2:00 P.M.
Lecture:
MWF 11:30-12:20 Neuberger Hall 387
Overview:
This course is on mathematical probability with foundations in analysis and measure theory. The presentation will include applications of stopping times, extreme value distributions, and Ito equations. We will also do some computing exercises to illustrate approximations and limit theorems.
Required Texts:
  1. R. Durrett, Probability: Theory and Examples 4th Edition, Cambridge University Press, 2013. Math 667 will cover approximately Chapters 1-3.2, with occasional forays into Oksendal for variety. Oksendal will be used more in 669.
  2. B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, 2010. (Earlier editions should work too.)
Prerequisites:
Advanced calculus and a course in probability or mathematical statistics.
Midterm Exam:
October 31: 1.5.4, 1.5.5, 1.7.2 and apply it to g(x)=x for X=[0, o-o).
Final Exam: Thursday December 11 12:30 PM (problems 3.2.12, 2.4.4(iii) with V lognormal (mu=.125, sigma=.25) and check conditions of SLLN for p in [0,1], Oksendal 2.18)
Homework:
  1. Friday Oct 3: 1.1.3, 1.1.5, 1.2.3, 1.2.4 (filter example)
  2. Friday Oct 10: 1.3.2, 1.3.3, 1.3.4, 1.4.1, 1.4.3(i) (Optional: show that the definition of a.s. convergence in Casella-Berger p. 234 is the same as the standard one in say Durrett, after dealing generously with some ambiguity in the C-B wording.)
  3. Friday Oct 17: 1.5.4, 1.5.10, 1.6.8, 1.6.10, 1.6.15
  4. Friday Oct 24: 1.7.1, 1.7.4, 2.1.1, 2.1.2, 2.1.7
  5. Friday Nov 7: 2.2.1, 2.2.2, 2.2.3(ii), 2.3.2, 2.3.3 (some solutions)
  6. Friday Nov 14: 2.4.4
  7. Friday Nov 21: 3.2.11, 3.2.13 (some solutions)
  8. Friday Dec 5: 3.3.8 



    
   September 2014   
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28 29 30              first class Monday 
                     
    October 2014    
Su Mo Tu We Th Fr Sa
          1  2  3  4  1.1-1.2
 5  6  7  8  9 10 11  1.3-1.4
12 13 14 15 16 17 18  1.5-1.6, Fatou's Lemma example 
19 20 21 22 23 24 25  1.7 2.1
26 27 28 29 30 31     2.2
                     
    November 2014   
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 2  3  4  5  6  7  8  2.3
 9 10 11 12 13 14 15  2.4
16 17 18 19 20 21 22  3.2 proof of Thm 3.2.2 
23 24 25 26 27 28 29  3.3 Thanksgiving Break 
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    December 2014   
Su Mo Tu We Th Fr Sa
    1  2  3  4  5  6  3.3 
 7  8  9 10 11 12 13  Final Exam Thursday 
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last updated: Nov 26 2014