Advanced Stochastic Processes

Team

Time and Place

Lecture: Fridays, 10am - 12pm, in HeHo 18, 220 (some specific dates can be found on Moodle)

Exercises: Wednesdays, 10am - 12pm, in HeHo 18, 220 (bi-weekly starting on the 27th of October - specific dates on Moodle)

Topics

This course is based on Chapters 4, 5 and 6 of the "Stochastics II" lecture notes from Evgeny Spodarev which you can find here. We expect the content of chapters 1, 2 and 3 to be known from the previous (German) course "Wahrscheinlichkeitstheorie and Stochastische Prozesse (WTSP)". More precisely, we will cover

Martingales
Lévy processes
Stationary processes in discrete time

Also, we shall discuss analytic, geometric and asymptotic properties of stochastic models to provide the students with knowledge related to statistical methods and simulation algorithms.

Prerequisites

This course assumes knowledge from the courses Elementary Probability Calculus and Statistics and Probability Theory and Stochastic Processes.

In order to be allowed to register for the exam, you will need to get 50% of the exercise points.

Type

2 hours lecture + 1 hour exercise.

Credit points: 4

Intended Audience

Elective module: Bachelor's and Master's students studying Mathematics, Mathematical Biometrics or Mathematical Economics.

Exam

We will have individual oral exams at the end of the semester. Specific dates will be announced on Moodle.

Literature

A list of suitable literature can be found here.