Format: Virtual Zoom Conference

Register to the workshop at Zoom Registration

Organizers: Krzysztof Bogdan, Arturo Kohatsu-Higa, 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 26-30 October 2020 focused on the interplay of Lévy-type processes with nonlocal partial differential equations and potential theory. The second workshop on 22-26 March 2021 is dedicated to statistical problems and simulation for jump processes. The workshops are organised as part of the Beethoven grant "Sensitivity Analysis of Nonlocal Operators with Applications to Jump Processes" carried out under the supervision of René Schilling and Krzysztof Bogdan.

Agenda:

Date: Mon 22-March-2021 -- Fri 26-March-2021
Format: Virtual Zoom Conference
Time: 3 talks a day: 10:00-11:00, 11:00-12.00 and 14:00-15:00 (GMT+1h)
In this workshop we want to focus on:

Schedule:

Times are given in Wroclaw-Dresden time (GMT+1h).

Monday, 22 Mar:

10:00-11:00

11:00-12:00

14:00-15:00

Tuesday, 23 Mar:

10:00-11:00

11:00-12:00

14:00-15:00

Wednesday, 24 Mar:

10:00-11:00

11:00-12:00

14:00-15:00

Thursday, 25 Mar:

10:00-11:00

11:00-12:00

14:00-15:00

Friday, 26 Mar:

10:00-11:00

11:00-12:00

14:00-15:00

Planned content and form of lectures:

  1. Arturo Kohatsu-Higa:
    • Simulation of Poisson random measures
    • Exact simulation methods for jump driven SDE's
    • Simulation methods for infinite activity Levy processes and their associated functionals
    • Interaction between simulation and theory
    Course structure: I will mostly concentrate on simulation methodology with associated theoretical results such as convergence results and their rate. I also plan to discuss the interaction between theory and applications. Some interesting and feasible open problems will be discussed, too.
  2. Andrea Pascucci: A class of Kolmogorov SPDEs and applications to stochastic filtering.