We cordially invite all students and PhD students interested in probability theory to a series of lectures entitled Exit times for random walks professor Vitalego Wachtela from the University of Bielefeld. Professor Wachtel is a recognized specialist in the field of stochastic processes with a particular focus on random walks. Lectures will be held on Tuesdays (4-6 p.m., EM room) and Thursdays (2-4 p.m., room 602) at the Institute of Mathematics of the University of Wrocław. The lecture Exit times for random walks can be counted as an (advanced mathematical) elective course. Credit will be based on an oral exam. The student will then receive 2 points for the lecture. ECTS.
Title of the lecture: Exit times for random walks
Lecture description:
The main purpose of the mini-course is to introduce classical and novel approaches to the study of first-passage times of random walks and Markov processes. I shall start with the classical Wiener-Hopf method, which allows one to obtain exact equalities for generating functions of first-passage times for one-dimensional random walks. This approach allows one not only to determine the tail behaviour of first-passage times, but also to prove various limit theorems for conditioned random walks. In this part, I will also discuss the notion of dual stopping times introduced by Greenwood and Shaked. In the second half of the course I will describe a new method, which allows asymptotic analysis of passage times for multidimensional walks with i.i.d. increments and for one-dimensional walks with independent but not necessarily identically distributed increments. This method uses only functional limit theorems for original walks. This fact also gives a possibility to use the method also for Markov chains.
Dates:
07.05.2024 4:15 p.m. – 6:00 p.m., room EM
09.05.2024 14:15 – 16:00, room 602
14.05.2024 4:15 p.m. – 6:00 p.m., room EM
16.05.2024 14:15 – 16:00, room 602
17.05.2024 11:15 – 13:00, (this date to be confirmed and room to be agreed)
21.05.2024 4:15 p.m. – 6:00 p.m. room EM
23.05.2024 14:15 – 16:00 room 602