**Stochastic Processes (****V3F1/F4F1****), summer term 2015**

Tuesdays 8 – 10, kleiner Hörsaal, Wegelerstraße 10

Fridays 10 – 12, kleiner Hörsaal, Wegelerstraße 10

Start of lecture: 7th of April

Start of tutorial classes: first week!

Lecture: Prof. Dr. Karl-Theodor Sturm

Exercises: Angelo Profeta

**Exams**

First exam: Sat 25.7.2015, 9:00 – 11:00, Wolfgang-Paul-Hörsaal, Kreuzbergweg 28

Second exam: Thu 24.9.2015, 9:00 – 11:00, Großer Hörsaal, Wegelerstr. 10

You need at least 50% of the points on the exercise sheets to be admitted to the exams.

**Tutorials **

Thu 10 - 12, 0.008: Alexander Rosenbaum

Thu 12 - 14, 0.011: Giovanni D'Urso

Thu 14 - 16, 0.008: Giovanni D'Urso

Fri 14 - 16, 0.008: Umar Adil

**Exercise sheets**

The exercise sheets will be handed out tuesdays during the lecture, and your solutions are due one week later. You may (and should) work in groups of 2. Besides your names, please also write down your matriculation numbers and the name of your tutor on the solution.

Exercise sheet 0 (discussed in first week)

Exercise sheet 1 (due 14.4.2015) (10.4.: corrected sign error in ex. 4)

Exercise sheet 2 (due 21.4.2015) (17.4.: corrected typo in ex. 3b))

Exercise sheet 3 (due 28.4.2015)

Exercise sheet 4 (due 5.5.2015)

Exercise sheet 5 (due 12.5.2015) (5.5.: added initial value in ex. 3)

Exercise sheet 6 (due 19.5.2015)

Exercise sheet 7 (due 2.6.2015) (19.5.: added range of q in ex. 3; 20.5.: modified ex. 2 to get elementary proof)

Exercise sheet 8 (due 9.6.2015) (6.6.: the chain in ex. 4 should be irreducible!)

Exercise sheet 9 (due 16.6.2015)

Exercise sheet 10 (due 23.6.2015) (19.6.: square missing in ex. 1b))

Exercise sheet 11 (due 30.6.2015) (23.6.: modified ex. 1c))

Exercise sheet 12 (due 7.7.2015) (1.7.: corrected ex. 4c))

**Topics**

- conditional expectation
- discrete-time Markov processes
- Brownian motion

**Literature**

There are many books that cover (at least some of) the topics of the lecture. You might have a look at:

Klenke – Wahrscheinlichkeitstheorie, Springer (there is also an english translation: "Probability Theory: A Comprehensive Course", Springer)

Durrett – Probability: Theory and Examples, Cambridge University Press

Norris – Markov chains, Cambridge University Press

Karatzas, Shreve – Brownian Motion and Stochastic Calculus, Springer

Revuz, Yor – Continuous Martingales and Brownian Motion, Springer

Bauer – Wahrscheinlichkeitstheorie, de Gruyter (there is also an english version: "Probability Theory", de Gruyter)

Old script of 2011