Syllabus for Math-571. Advanced Probability Theory. Spring 2007.
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Course:
Math-571. Advanced Probability Theory.
Spring 2007.
Prerequisite:
Prerequisite: MATH 447 or 501, and MATH 506 or
consent of instructor.
Schedule
:
T. R.: 8:00-10:00 a.m. Room: LN 2201.
Instructor: Miguel A. Arcones.
Office
: LN-2229.
Office hours
: T. H: 10:00-11:00 a.m.,
or by appointment. If you need to contact me or have any questions,
please e-mail me at: arcones@math.binghamton.edu.
Grading
: The grades for the course will come from
homeworks, class attendance and class participation.
Course description:
Measure theoretic
probability. Axiomatic foundations.
Caratheodory extension theorem. Lebesgue integration.
Random variables. Types of convergence. Law of large
numbers. Central limit theorem. Characteristic
functions. Infinite divisibility and stable laws. Conditional probability
and expectation. Martingales. Other topics as time permits.
Credit hours:
5 cr.
Course materials: You can find the syllabus and
the homeworks in my web page:
http://www.math.binghamton.edu/arcones/571/.
References
:
- Athreya, K. B. and Lahiri, S. N. (2006).
Measure Theory and Probability Theory. Springer.
- Durrett, R. A. (1996). Probability: Theory and
Examples. Duxburry Press.
- Resnick, S. I. (1999). A Probability Path. Birkahuser.
- Laha, R. G. and Rohatgi, V. K. (1977). Probability Theory. Wiley.
- Chow, Y. S. and Teicher, H. (1978). Probability
Theory. Springer.
- Dudley, R. M. (1989). Real Analysis and Probability. Wadsworth and Brooks/Cole.
- Billingsley, P. (1968). Convergence of Probability Measures. Wiley.
- Loève, M. (1977). Probability Theory I and II. Springer.
- Ash, R. B. (1972). Real Analysis and Probability. Academic Press.
- Royden, H. L. (1968). Real Analysis. Macmillan.
- Folland, G. B. (1999). Real Analysis. Wiley.
Lecture days
|
Janu |
Janu |
Febr |
Febr |
Febr |
Febr |
Marc |
Marc |
Marc |
Marc |
Apr |
Apr |
Apr |
Apr |
Apr |
May |
| Tuesday |
23 |
30 |
6 |
13 |
20 |
27 |
6 |
13 |
20 |
27 |
p.o. |
10 |
17 |
24 |
1 |
8 |
| Thursday |
25 |
1 |
8 |
15 |
22 |
1 |
s.b. |
15 |
22 |
29 |
p.o. |
12 |
19 |
26 |
3 |
10 |
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