# Stochastics II

Lecturer

Prof. Dr. Volker Schmidt

Teaching assistant

Matthias Neumann

## Time and place

Lecture

Tuesday 10-12 am (H14) and Thursday 10-12 am (H14)

Exercise class

Wednesday 4-6 pm (H14)

## Type

4 hours lecture and 2 hours exercise

## Prerequisites

Elementary probability course  ("Elementare Wahrscheinlichkeitsrechnung und Statistik") and Stochastics I.

## Intended audience

Bachelor students in "Mathematik",  "Mathematische Biometrie" and "Wirtschaftsmathematik".

Mater students in "Mathematik",  "Mathematische Biometrie" and students in "Master of Finance".

## Content

The lecture gives an introduction in various classes of stochastic processes. The main topics of the lecture
are

• Conditional expectation and conditional probability
• Counting processes and renewal processes
• Markov processes with discrete state space
• Martingales
• Brownian motion
• Levy processes
• Poisson point processes

Especially analytic, geometric and asymptotic properties of the models named above are discussed in the lecture. These properties are the basis for statistical methods and model simulation. The topics allow a high number of practical applications. Moreover, the topics of the lecture are chosen in such a way, that they can be easily linked to research projets of the Institute of Stochastics. Thus, the lecture is a good preparation for joining these projects in form of a practicum or Bachelor and Master thesis.

## Exam

The first exam will take place at February 20 (8 am), 2015.

The second exam will take place at April 1 (9 am), 2015.

In order to participate in the final exam, it is necessary to earn 50% of the points on all problem sheets.

## The exam is corrected!

You can find the number of points you obtained in the SLC as an extra exercise sheet (marked as "Prüfungsleistung"). The associated marks are indicated in the following tabular:

Mark   Points
1,045 - 39
1,338.5 - 36.5
1,736 - 34
2,033.5 - 31.5
2,331 - 29.5
2,729 - 27.5
3,027 - 25.5
3,325 - 23.5
3,723 - 21.5
4,021 - 19
5,018,5 - 0

## Literature

• Breiman, L.
Probability

• Daley, D.J., Vere-Jones, D.
An Introduction to the Theory of Point Processes, vol. I & II
Springer, New York (2005/8)

• Grimmett, G., Stirzaker, D.
Probability and Random Processes
Oxford University Press, Oxford (2001)

• Illian, J., Penttinen, A., Stoyan, H., Stoyan, D.
Statistical Analysis and Modelling of Spatial Point Patterns
Wiley, Chichester (2008)

• Kingman, J.F.C.
Poisson Processes
Oxford University Press, Oxford (1993)

• Lefebvre, M..
Applied Stochastic Processes
Springer, Berlin (2007)

• Prabhu, N.U.
Stochastic Processes: Basic Theory and Its Applications
World Scientific, Singapore (2007)

• Resnick, S.I.
Birkhäuser, Boston (1992)

• Rolski, T., Schmidli, H., Schmidt, V., Teugels, J.
Stochastic Processes for Insurance and Finance
J. Wiley & Sons, Chichester (1999)

• Serfozo, R.
Basics of Applied Stochastic Processes
Springer, Berlin (2009)

# Lecturer

• Office hours: on appointment
• Phone: +49 (0)731/50-23532
• Homepage

# Teaching assistant

• Office hours: on appointment
• Phone: +49 (0)731/50-23617
• Homepage

# Aktuelles

The second exam is corrected! You can find the number of points you obtained in the SLC as an extra exercise sheet (marked as "Prüfungsleistung"). The associated marks are indicated in a tabular (see left side).

The second exam takes place in H1/ O25.

The post-exam review will take place on Thursday, March 5 from 2 to 3 pm in room E31 in Helmholtzstr. 20. Alternatively it is possible to come to the post-exam review of the second exam which takes place at April 9 from from 2 to 3 pm in room E60 in Helmholtzstr. 18.

The final exam is corrected! You can find the number of points you obtained in the SLC as an extra exercise sheet (marked as "Prüfungsleistung"). The associated marks are indicated in a tabular (see left side).

Participants of the final exam will be allowed to bring one handwritten A4 sheet (both sides) containing useful results from the lecture and exercise classes. Copies and printouts will not be allowed.