International Seminar on SDEs and Related Topics


    This online seminar takes place every second Friday at
   12:30 UTC during European daylight saving times        11:30 UTC otherwise    

  12:30 noon       1:30 pm       2:30 pm       8:30 pm (7:30 pm from Apr 08 on)    
    London        Berlin, Paris         Helsinki         Beijing    

                    Zoom link       Meeting ID: 618 9100 7917

No registration required. To get an e-mail reminder before each event write to sde-seminar[at]jyu.fi.


Organisers

  • Stefan Ankirchner   (FSU Jena, Germany)
  • Christian Bender   (Saarland University, Germany)
  • Rainer Buckdahn   (Universite de Bretagne Occidentale, France)
  • Dan Crisan   (Imperial College London, UK)
  • Christel Geiss   (University of Jyväskylä, Finland)
  • Stefan Geiss   (University of Jyväskylä, Finland)
  • Céline Labart   (Université Savoie Mont-Blanc, France)
  • Juan Li   (Shandong University, China)
  • Andreas Neuenkirch   (University of Mannheim, Germany)
  • Shige Peng   (Shandong University, China)
  • Adrien Richou   (University of Bordeaux, France)

Schedule 2021


Oct 29, 2021

Peter Friz (TU Berlin and WIAS Berlin):           Poster:           Video   (expires April 2022)

On rough SDEs

Abstract: A hybrid theory of rough stochastic analysis is built that seamlessly combines the advantages of both Itô's stochastic - and Lyons' rough differential equations. A major role is played by a new stochastic variant of controlled rough paths spaces, with norms that reflect some generalized stochastic sewing lemma, and which may prove useful whenever rough paths and Itô integration meet. We will mentioned several applications. Joint work with Antoine Hocquet and Khoa Lê (both TU Berlin).


Nov 12, 2021

Xunyu Zhou (Columbia University, New York):           Poster:           Video   (expires April 2022)

Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space:
A Martingale Lens

Abstract: We propose a unified framework to study policy evaluation (PE) and the associated temporal difference (TD) methods for reinforcement learning in continuous time and space. Mathematically, PE is to devise a data-driven Feynman--Kac formula without knowing any coefficients of a PDE. We show that this problem is equivalent to maintaining the martingale condition of a process. From this perspective, we present two methods for designing PE algorithms. The first one, using a "martingale loss function", interprets the classical gradient Monte-Carlo algorithm. The second method is based on a system of equations called the "martingale orthogonality conditions". Solving these equations in different ways recovers various classical TD algorithms, such as TD, LSTD, and GTD. We apply these results to option pricing and portfolio selection. This is joint work with Yanwei Jia.


Nov 26, 2021

Michael Scheutzow             Poster:     SlidesVideo   (expires May 2022)
(Technische Universität Berlin):

Generalized couplings and stochastic functional differential equations

Abstract: We provide an introduction to generalized couplings and present a recent result [contained in S.: Couplings, generalized couplings and uniqueness of invariant measures. ECP, 2020] which says that the existence of a generalized coupling for a Markov chain implies uniqueness of an invariant probability measure even if the state space is just a metric space without requiring separability or completeness as in previous works. The proof turns out to be rather elementary. We show how this result can be applied to show uniqueness of an invariant measure for the solution process of a stochastic functional differential equation (SFDE) and we show how generalized couplings can be employed to show weak uniqueness of solutions of an SFDE with Hölder continuous coefficients.
Parts of the talk are based on joint work with Alex Kulik (Wroclaw).


Dec 10, 2021

Nizar Touzi (CMAP & Polytechnique Paris):           Poster:

Entropic mean field optimal planning

Abstract: The problem of optimal planning was introduced by P.-L. Lions in the context of a mean field game, by fixing a target distribution in the Focker-Planck equation and relaxing the boundary condition in the HJB equation. We analyze an extension of this problem to the path-dependent setting which has remarkable connections with optimal transport and optimal incentive theory in economics. We provide a general characterization of mean field optimal planning solutions, and we solve explicitly the minimum entropy optimal planning problem.


Schedule 2022


Jan 14, 2022

Arturo Kohatsu-Higa (Ritsumeikan University, Kusatsu): TBA

Jan 28, 2022

Denis Talay (INRIA & École Polytechnique): TBA

Feb 11, 2022

Mireille Bossy (Sophia Antipolis, France ): TBA

Feb 25, 2022 @ 12:30 UTC, one hour later than usual!

Xin Guo (University of California at Berkeley): TBA

Mar 11, 2022

Lukasz Szpruch (University of Edinburgh): TBA

Mar 25, 2022 @ 12:30 UTC, one hour later than usual!

Jianfeng Zhang (University of Southern California): TBA

Apr 08, 2022

Krzysztof Bogdan (Wrocław University of Science and Technology): TBA

Apr 22, 2022

TBA

May 06, 2022

François Delarue (Université de Nice Sophia-Antipolis): TBA

May 20, 2022

Ying Hu (Université de Rennes 1, CNRS): TBA


Contact and links

    Stefan Geiss: stefan.geiss[at]jyu.fi or stefanfriedrich.geiss[at]gmail.com
    The online seminar is hosted by the Department of Mathematics and Statistics (University of Jyväskylä) and supported by the journal Probability, Uncertainty and Quantitative Risk.