Alejandro Caicedo
Mathematisches Institut
LMU München
Wintersemester 2021/22

Stochastic processes

Wintersemester 2021/22

Description

Registration

Target Audience

Times and Location

Literature

Exercises

Exam

1. Description

Welcome to the course on stochastic processes! The course presents some elements of the mathematical foundation for continuous-time stochastic processes. Central topic in this course is the theory of Feller Processes. A major theme is the Hille-Yoshida theory, which provides a correspondence between Feller Processes, semigroups and a class of linear operators (the "generators" of the processes). We will prove this correspondance, and subsequently properties of the operator translate into properties of the processes and vice versa. We then discuss a number of specific examples of Feller processes that are of great importance in probability theory: Brownian motion, Lévy processes, continuous-time Markov chains and interacting particle systems.

2. Registration

Subscribing to Moodle required.

The enrollement key is: Stochastic2022

Please subscribe to this course on Moodle via this link: Moodle page

3. Target Audience

The course is intended for master students in Mathematics, Finance- and Insurance Mathematics and TMP.

4. Times and Location

We intend to make this a life course taking place at the Mathematics Department, Theresienstrasse 39.

Lecture:	Monday 12:00-14:00 c.t.	B 0004	Markus Heydenreich
	Thursday 12:00-14:00 c.t.	B 0004
Exercise Class:	Wednesday 14:00-16:00 c.t.	B 0004	Alejandro Caicedo

5. Literature

The main reference for this course is

• Thomas M. Liggett, Continuous time Markov processes.

The following is a list of other relevant literature.

• L.B. Koralov and Ya. Sinai, Theory of Probability and Random Processes, 2nd edition, Springer 2010.
An alternative presentation of the material
• A. Klenke, Probability Theory, Springer 2014.
An even different presentation of the material, also available in German
• P. Mörters, Y. Peres, Brownian Motion, Cambridge University Press 2010. .

Link Specifically for the chapter on Brownian motion

• R. Durrett, Probability. Theory and Examples, 4th edition, Cambridge University Press 2010.

Link (contains all the basics in probability theory)

More literature is provided during the course.

6. Exercises

The Exercises will be posted here.

7. Exam

Oral exam in February 2022. Re-take in April 2022.