Organiser

Lecturer
Prof. Dr. Evgeny Spodarev

Lecturer
Dr. Michael Juhos

Time and place

The course will be organised via Moodle. Click here for the Moodle course.

Lecture
Monday, 10:00–12:00, N25 H3
Thursday, 10:00–12:00, N25 H3

Exercise
Monday, 16:00–18:00, N25 H3

Length

4 hours lecture and 2 hours exercise

Prerequisites

Analysis I and II, Linear Algebra I and II, Elementary Probability and Statistics.

It is recommended to have attended the lecture Measure Theory.

Target audience

Bachelor Mathematics, Mathematics and Management, and Mathematical Biometry.

Contents

The lecture is a continuation of the lecture “Elementary Probability and Statistics”. In addition, stochastic processes and important examples are introduced.

The lecture focuses on the following topics:

• Lebesgue integral
• Conditional expectation
• Characteristic function
• Types of convergence
• Limit theorems
• Introduction to the theory of random functions
• Elementary stochastic processes, e. g. Brownian motion and Poisson process

Lecture notes

The lecture notes can be downloaded here.

Exam

The exams will take place on 01/08/2025 and 06/10/2025.

The prerequisite for participation in both exams is passing the prerequisites. At least 50 % of the exercise points must be achieved.

Please register for the exam on the university portal in good time before the exam (only possible if you have passed the prerequisites).