Veranstaltungen

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Dienstag, 11.05.2021, 15:00 Uhr (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Paul Hager, Technische Universität Berlin:
Optimal stopping with signatures (online talk)
mehr ... Veranstaltungsort
Online Event

Abstrakt
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process. We consider classic and randomized stopping times represented by linear and non-linear functionals of the rough path signature associated to the underlying process, and prove that maximizing over these classes of signature stopping times, in fact, solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a (deterministic) optimization problem depending only on the (truncated) expected signature. By applying a deep neural network approach to approximate the non-linear signature functionals, we can efficiently solve the optimal stopping problem numerically. The only assumption on the underlying process is that it is a continuous (geometric) random rough path. Hence, the theory encompasses processes such as fractional Brownian motion, which fail to be either semi-martingales or Markov processes, and can be used, in particular, for American-type option pricing in fractional models, e.g. on financial or electricity markets. This is a joint work with Christian Bayer, Sebastian Riedel and John Schoenmakers.

Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Dienstag, 11.05.2021, 15:15 Uhr (Online Event)
Oberseminar Nonlinear Dynamics
Alicia Dickenstein, U Buenos Aires:
Algebra and geometry in the study of enzymatic networks? (online talk)
mehr ... Veranstaltungsort
Online Event

Abstrakt
I will try to show in my lecture that the question in the title has a positive answer, summarizing recent mathematical results about signaling networks in cells obtained with algebro-geometric tools.

Weitere Informationen
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSll3TjAxV1U1S2xFQT09.

Veranstalter
Freie Universität Berlin
WIAS Berlin
Mittwoch, 12.05.2021, 11:30 Uhr (Online Event)
Seminar Interacting Random Systems
Tal Orenshtein, WIAS Berlin/TU Berlin:
Rough walks in random environment
mehr ... Veranstaltungsort
Online Event

Abstrakt
Random walks in random environment (RWRE) have been extensively studied in the last half-century. Functional central limit theorems (FCLT) hold in some prototypical classes such the reversible and the ballistic ones. The latter are treated using rather different techniques; Kipnis-Varadhan's theory for additive functionals of Markov processes is applicable in the reversible case whereas the main feature exploited in the ballistic class is a regeneration structure. Rough path theory is a deterministic theory which extends classical notions of integration to singular integrators in a continuous manner. It typically provides a framework for pathwise solutions of ordinary and partial stochastic differential equations driven by a singular noise. In the talk we shall discuss FCLT for additive functionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels. The first one is the Brownian motion, whereas in the second we see a new feature: it is the iterated integral of the Brownian motion perturbed by a deterministic linear function called the area anomaly. The aforementioned classes of RWRE are covered as special cases. The results provide sharper information on the limiting path. In addition, the construction of new examples for SDE approximations is an immediate application. Based on collaborations (some are still in progress) with Johannes Bäumler, Noam Berger, Jean-Dominique Deuschel, Olga Lopusanschi, Nicolas Perkowski and Martin Slowik.

Weitere Informationen
Seminar Interacting Random Systems (Online Event)

Veranstalter
WIAS Berlin
Mittwoch, 12.05.2021, 15:15 Uhr (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Thomas Eiter, WIAS Berlin:
Leray--Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation (online talk)
mehr ... Veranstaltungsort
Online Event

Abstrakt
Subject of the talk is a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba--Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. After a discussion of the model, the existence of global-in-time weak solutions, which satisfy an energy inequality, is shown under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.

Weitere Informationen
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin