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Tuesday, 15.01.2019, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. A. Gasnikov, Moscow Institute of Physics and Technology, Russische Föderation:
Adaptive accelerated stochastic gradient descent
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics

Host
WIAS Berlin
Tuesday, 15.01.2019, 15:15 (FU Berlin)
Oberseminar Nonlinear Dynamics
Prof. W. Hsia, National Taiwan University:
On the mathematical analysis of the synchronization theory with time-delay effect
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130

Abstract
In this lecture, we will introduce a newly developed mathematical theory on the synchronized collective behavior of the Kuramoto oscillators with time-delayed interactions and phase lag effect. Both the phase synchronization and frequency synchronization are in view. This is joint work with Bongsuk Kwon, Chang-Yeol Jung and Yoshihiro Ueda.

Host
Freie Universität Berlin
WIAS Berlin
Wednesday, 16.01.2019, 10:00 (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. M. Trabs, Universität Hamburg:
Parameter estimation for stochastic PDEs based on discrete observations in time and space
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Motivated by random phenomena in natural science as well as by mathematical finance, stochastic partial differential equations (SPDEs) have been intensively studied during the last fifty years with a main focus on theoretical analytic and probabilistic aspects. Thanks to the exploding number of available data and the fast progress in information technology, SPDE models become nowadays increasingly popular for practitioners, for instance, to model neuronal systems or interest rate fluctuations to give only two examples. Consequently, statistical methods are required to calibrate this class of complex models. We study the parameter estimation for parabolic, linear, second order SPDEs observing a mild solution on a discrete grid in time and space. Focusing first on volatility estimation and assuming a high-frequency regime in time, we provide an explicit and easy to implement method of moments estimator based on squared time increments of the process. If the observation frequency in time is finer than in space, the estimator is consistent and admits a central limit theorem. This is established moreover for the estimation of the integrated volatility in a semi-parametric framework. In a second step, we consider not only time increments of the solution field but also space increments as well as space-time increments. This allows for the construction of estimators which are robust with respect to the sampling regime, i.e., they are also applicable if the observation grid in space is finer than in time. Finally, we discuss the estimation of the parameters in the differential operator which determines the SPDE. This talk is based on joint works with Markus Bibinger and Florian Hildebrandt.

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Wednesday, 16.01.2019, 13:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
T. Keil, WIAS Berlin:
Optimal control of a coupled Cahn--Hilliard--Navier--Stokes system with variable fluid densities
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
This talk is concerned with the optimal control of two immiscible fluids with non-matched densities. For the mathematical formulation of the fluid phases, we use a coupled Cahn-Hilliard/Navier-Stokes system by Abels, Garcke and Grün, which involves a variational inequality of fourth order. We verify the existence of solutions to a suitable time discretization of the system and formulate an associated optimal control problem. We further discuss the differentiability properties of the control-to-state operator and the corresponding stationarity concepts and present strong stationarity conditions for the problem. This enables us to provide a numerical solution algorithm which terminates at an at least C-stationary point which - in the best case - is even strongly stationary. The method is based on an adaptation of a bundle-free implicit programming approach for MPECs in function space presented by Hintermüller and Surowiec in 2016.

Further Informations
Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations

Host
WIAS Berlin
Wednesday, 16.01.2019, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. J. Rehberg, WIAS Berlin:
An extrapolation for the Lax-Milgram isomorphism for second order divergence operators
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In 1989 Gröger generalized the famous isomorphy result of Meyer to a setting which allows for mixed boundary conditions. We again generalize Gröger's result to much more general geometric configurations.

Host
Humboldt-Universität zu Berlin
WIAS Berlin