Stochastic Processes
 

For the  lecture notes, click here. Contradicting earlier announcements, I have decided that the
exam will be written, not oral. The level of the questions will be comparable to the exercises
made throughout the course.

The lectures will take place (from now on) in room K11 in the Math-building.
 

In case you have questions, please contact me or Alexis Gillett. Alexis' email address is
ajg@math.vu.nl, and his homepage is www.math.vu.nl/~ajg.
 
 

The Exam is on june 13, 14-17 in room S201 at the VU in Amsterdam.
 
 

Material covered during lectures

feb. 7: Until Theorem 1.4.4 (inclusive), but we have not proved Theorem 1.3.3 yet.
feb 14: We filled in all details that were not done earlier, and also gave an alternative
direct construction of Brownian Motion (Levy interpolation construction); this alternative
construction is not in the notes.
feb. 21: We finished 1.4, 1.5 and made a start with 1.6.
feb. 28: We finished Chapter 1.
march 7: Started the theory about discrete time martingales.
march 14: Almost finished discrete time martingales.
march 21: Finish discrete time martingales, that is, finish 2.2 (and do exercises).
april 11: We discussed the theory of continuous time martingales, Section 2.3.
april 18: Section 2.4.
april 25: Do exercises from 2.5; start of Markov Process theory.
may 23-30:  Section 2.6-2.8 of distributed notes; Section  3.1-3.6 of distributed notes.

no lectures on may 2/9/16.

Exercises

The dates here refer to the day on which these exercises will be discussed in class.

feb. 14:  1.7.4, 1.7.5, 1.7.7, 1.7.9, 1.7.10, 1.7.11.
feb 28:  1.7.14 - 1.7.24.
march 21: 2.5.1 - 2.5.6; 2.5.11, 2.5.12.
april 25: 2.5.8-9, 2.5.13-15; Prove theorem 2.3.11 and Theorem 2.3.15; Deduce the limits
to infinity from the limits to 0 in Theorem 2.4.5;
may 30: 2.7.1(a); 2.8.1; 3.3.1; 3.4.1; 3.6.1; 3.6.3.