Probability Seminar Essen
Winterterm 2021/22: The seminar will start on October 12th.
Most of the talks take place via Zoom at this link
Tatiana Orlova (University of Duisburg-Essen)
Spectral Bootstrap confidence bands for Lévy-driven moving average processes
This report will consider the problem of constructing bootstrap confidence intervals for the Lévy density of the driving Lévy process based on highfrequency observations of a Lévy-driven moving average processes. Using a spectral estimator of the Lévy density, we propose a novel implementations of multiplier bootstraps to construct confidence bands on a compact set away from the origin. We also provide conditions under which the confidence bands are asymptotically valid.
Philipp Petersen (University of Vienna)
Functions with structured singularities appear in many application domains. For example, in image processing, jumps in intensity value are often associated to the boundaries of physical objects and appear along curves. In classification problems, decision boundaries are often assumed to possess a certain regularity. Finally, in the modelling of physical processes, such as fracture mechanics, singularities naturally appear. In the associated application areas, it is then necessary to finely resolve the singularities. We will analyse the extent to which deep neural networks are affected by discontinuous target functions if the discontinuity admits certain regularities. We will demonstrate that deep neural networks are surprisingly efficient at resolving discontinuities of potentially very high dimensional functions.
Adrián González Casanova (UNAM)
[The talk takes place on site]
Lambda Selection and where to find it
There are many ways in which two populations can compete for resources and this leads to different forms of selection. A Lambda coalescent is a beautiful mathematical object that describes the genealogy of populations with skewed offspring distributions. We will discuss selection in the context populations in the Lambda universality class. Along the way, we will talk about a novel technique to relate coalescent processes with branching processes and about duality of Markov processes.
Most of the talk is based on joint work with Maria Emilia Caballero (UNAM, Mexico) and Jose Luis Perez (CIMAT, Mexico)
Yuri Kabanov (Lomonosov MSU and Université Bourgogne Franche-Comté)
Ruin probabilities for models with investments
We present several new results on asymptotics of ruin probabilities for models of insurance company investing its reserve in a risky asset including Sparre Andersen model with investment and models where the stock price has stochastic volatility.
Yan Dolinsky (Hebrew University of Jerusalem)
Khoa N Le (TU Berlin)
[The talk takes place on site]
Taming singular SDEs numericallyWe consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusion coefficient is uniformly elliptic, Hölder continuous and weakly differentiable in the spatial variables while the drift satisfies the Ladyzhenskaya--Prodi--Serrin condition, as considered by Krylov and Röckner (2005). In the discrete scheme, the drift is tamed by replacing it by an approximation. A strong rate of convergence of the scheme is provided in terms of the approximation error of the drift in a suitable and possibly very weak topology. A few examples of approximating drifts are discussed in detail. The parameters of the approximating drifts can vary and be fine-tuned to achieve the standard 1/2-strong convergence rate with a logarithmic factor. Joint work with Chengcheng Ling, arXiv:2110.01343
Thomas Kruse (University of Giessen)
Larisa Yaroslavtseva (University of Passau)
David Criens (University of Freiburg)
[The talk takes place on site]Tba.
Kristin Kirchner (TU Delft)Tba.