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Format: free Zoom webinar

Register to the workshop at Zoom Webinar Registration

Organizers: Krzysztof Bogdan, Alex Kulik, René Schilling

Nonlocal organizers: David Berger, Krzysztof Bogdan, Jakub Minecki

Host Institutions:

WUST Faculty of Pure and Applied Mathematics

TUD Faculty of Mathematics Institute of Mathematical Stochastics

Comments and inquiries: nomp@pwr.edu.pl

Many real-life phenomena, like weather patterns or prices of stocks exhibit jump-type behavior. In fact, from a certain mathematical perspective, the jump-type phenomena–understood as Lévy-type stochastic processes–may be considered more general than the continuous phenomena–understood as diffusion processes. The theory of Lévy-type processes belongs to the field of stochastic processes. However, because of numerous and deep links with other areas of mathematics, it is also significant for potential theory, the theory of nonlocal partial differential equations, as well as statistics and financial mathematics. The workshop "Nonlocal Operators and Markov Processes" offers a view toward the field accessible to people of different backgrounds. The first workshop on Oct 26-30 focuses on the interplay of Lévy-type processes with nonlocal partial differential equations and potential theory. The workshops are organised as part of the Beethoven grant titled "Sensitivity Analysis of Nonlocal Operators with Applications to Jump Processes". The project is being carried out under the supervision of René Schilling and Krzysztof Bogdan. The next workshop planned for the year 2021 will be dedicated to statistical problems related to jump processes.

Schedule

All times are given in Wroclaw-Dresden time, which will be GMT+1h during the workshop (check the current time in Wroclaw). Note that lectures on Monday and Friday start at a different time than on Tuesday-Thursday.

Monday, 26 Oct:

15:45

16:00-16:45

Chair:

Courses

Opening of the workshop

Franziska Kühn, Lévy-type processes 1 [video|slides]

Krzysztof Bogdan

Tuesday, 27 Oct:

15:00-15:45 and 16:00-16:45

17:00-17:45

Chair:


Xavier Ros-Oton, Boundary regularity for nonlocal operators 1 [video 1|video 2|slides]

Franziska Kühn, Lévy-type processes 2 [video|slides]

René Schilling

Wednesday, 28 Oct:

15:00-15:45 and 16:00-16:45

17:00-17:45

Chair:


Xavier Ros-Oton, Boundary regularity for nonlocal operators 2 [video 1|video 2|slides]

Mateusz Kwaśnicki, Potential theory of Markov processes 1 [video|slides]

Tomasz Klimsiak

Thursday, 29 Oct:

15:00-15:45 and 16:00-16:45

17:00-17:45

Chair:


Xavier Ros-Oton, Boundary regularity for nonlocal operators 3 [video 1|video 2|slides]

Mateusz Kwaśnicki, Potential theory of Markov processes 2 [video|slides]

Katarzyna Pietruska-Pałuba

Friday, 30 Oct:

10:15-11:00

Chair:

11:15-12:00

Chair:

12:15-13:00

Chair:

Recent Topics and Developments (note different time)

Enrico Valdinoci, The Bernstein technique for integrodifferential equations [video|slides]

Tomasz Grzywny

Bartłomiej Dyda, On fractional Hardy inequalities [video|slides]

Luz Roncal

Alex Kulik, Parametrix technique for complicated Lévy-type models [video|slides]

Arturo Kohatsu-Higa