WIAS Berlin Mittwoch, 01. Whenever the modelling of random processes in biology, finance or physics requires to incorporate jumps, Levy processes are one of the building blocks under consideration. Consequently, their statistical analysis attracted much attention in the last decades. days well understood nonparametric estimation of the characteristic triplet of a univariate Levy process based on low frequent observations. posed, where the degree of illposedness is determined by the characteristic triplet itself. changed Levy process at equidistant time points or, similarly, if we observe the Levy process at random sampling times. Indeed, in the latter two observation schemes faster rates can be achieved, especially allowing for polynomial convergence rates for the volatility.
Levy processes, focusing on the estimation of the volatility matrix. rank condition is imposed. For the volatility matrix estimator we moreover derive convergence rates. These reect surprising phenomena which do not occur in the one dimensional setting.
This talk is based on an ongoing joint work with Denis Belomestny. Universität zu Berlin WIAS Berlin Dienstag, 30. WIAS Berlin Dienstag, 30. WIAS Berlin Donnerstag, 25. Recent research suggests that the compression modulus of organic tissue is sensitive to changes of tissue pressure. provides a means to map the amplitudes of externally stimulated mechanical pressure waves and has proven its potential to differentiate between physiological states of different tissue pressure.
The interpretation of the results thus far has relied on an effective medium model. poroelastic theory can provide an explanation for the interaction between tissue pressure and the mechanical properties of tissue. However, quantification of the poroelastic parameters from MRE data still poses a challenge. WIAS Berlin Mittwoch, 24. Universität zu Berlin Mittwoch, 24. Forschungsseminar Mathematische Statistik Prof.
Electricity price forecasting is becoming increasingly relevant in the competitive energy markets. stationary data, the estimation is conducted over an interval of local homogeneity, over which the time varying data generating process can be approximated by an FAR model with constant operators. The local interval is identified in a sequential testing procedure. Simulation study illustrates good finite sample properties of the proposed AFAR modeling. Real data application on forecasting California electricity daily price curves demonstrates a superior accuracy of the proposed AFAR modeling compared to several alternatives.
Universität zu Berlin Universität Potsdam Dienstag, 23. WIAS Berlin Dienstag, 23. Seminar Nichtlineare Optimierung und Inverse Probleme Prof. Mechanical components fail under cyclic loading due to fatigue of the materials. This process is highly stochastic as the time to the formation of mesoscopic cracks is subject to a statistical scatter of one order of magniture in lab experiments.
temporal point processes with intensity depending locally on the mechanical load situation. This allows to compute failure probabilities at a given number of load cycles. survey is given about experimental calibration and validation of these models, numerical implementation and their applications to gas turbine design. In mechanical design, reliability is one of the main design objectives. The mathematical quest thus is to find a shape for the component such that the failure probability is minimized. This optimization task can be understood as an optimal control problem with the elasticity PDE as the state equation and the boundary of the shape as control parameter.
proof for the existence of optimal shapes within certain regularity classes of the boundary is given using strong solutions and uniform Schauder estimates. WIAS Berlin Freitag, 19. Seminar Partielle Differentialgleichungen Prof. WIAS Berlin Donnerstag, 18. Forschungsseminar Mathematische Modelle der Photonik Dr. Universität zu Berlin WIAS Berlin Donnerstag, 18. WIAS Berlin Mittwoch, 17. Veranstaltungsort Technische Universität, Straße des 17. In this talk, we will take a look at some systems of interacting particles on the real line, where the only spatial structure that is relevant for the dynamics is the relative order of the particles.
organized criticality at a critical point that marks the boundary between an interval where all particles are eventually removed and an interval where particle stay in the system forever. Universität zu Berlin Technische Universität Berlin Universität Potsdam Mittwoch, 17. Veranstaltungsort Technische Universität, Straße des 17. range and large amplitude. We illustrate that also the FKPP model is a limit of a particle system with certain branching mechanism. the porous medium equation with proliferation. This is based on ongoing research with Franco Flandoli. Universität zu Berlin Technische Universität Berlin Universität Potsdam Mittwoch, 17. Universität zu Berlin Mittwoch, 17. Universität zu Berlin Universität Potsdam Dienstag, 16. Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics Prof.
WIAS Berlin Dienstag, 16. Seminar Numerische Mathematik Prof. Parallel algorithms with hybrid MPI and OpenMP implementations for a geometric multigrid solver in a nite element scheme will be presented in this talk. In particular, the mesh partitioning, the nite element mappers and communicators on a hierarchy of multigrid mesh will be discussed. Further, a multicolor strategy in the smoothing steps of the multigrid solver, parallel restrictions and prolongations using halo cells will be discussed.
WIAS Berlin Dienstag, 16. Seminar Nichtlineare Optimierung und Inverse Probleme Dr. In inverse problems one wants to find unknown parameters or structures by indirect measurements. human torso, from line integrals of some form of radiation that travelled through the object. bone, liver, lung, etc. their location and their shape.
Shah type functional for the simultaneous reconstruction and segmentation of an object from tomography data. WIAS Berlin Donnerstag, 11. Forschungsseminar Mathematische Modelle der Photonik Dr. Universität zu Berlin WIAS Berlin Donnerstag, 11. Seminar Numerische Mathematik Prof. diffusion equations are considered.
The steady case is reviewed and local error bounds are obtained for general order finite element methods. For the evolutionary problem, local bounds are obtained when the SUPG method is combined with the backward Euler scheme. The arguments used in the proof lead to estimates for the stabilization parameter that depend on the length on the time step.
The numerical experiments show that local bounds seem to hold true both with a stabilization parameter depending only on the spatial mesh grid and with other time integrators. WIAS Berlin Mittwoch, 10. Universität zu Berlin Mittwoch, 10. The idea is to freeze the measures support by allowing the cardinalities of the support sets to be large enough. We propose new different numerical approaches to solve this problem. We generalize the approach by Cuturi and obtain a sharp bound on the rate of convergence. dual methods for these problems and we need to choose optimal relation between the precision of solution for the inner problem and the precision of solution of the whole problem. obtain the exact solution of the inner problem we have to properly choose the method for external problem which have the ability to work with inexact oracle.
This context is interesting in case when we have to find a Wb of huge number of empirical measures. Universität zu Berlin Universität Potsdam Donnerstag, 04. Seminar Numerische Mathematik Dr. The talk consists of two parts. The first part of the talk is dedicated to thin conducting sheets which are commonly used in the protection of electronic devices. The domain of computation is the thin metallic sheet, the surrounding air and other metallic or isolating parts. on triangular or tetrahedal cells. whose size depends on the frequency and may become smaller than the sheet thickness.
basis functions in thickness direction. The basis functions are defined hierarchically in the spirit of Vogelius and Babuska by an hierarchy of ordinary differential equations in thickness directions. enters the variational formulation. posedness and estimate for straight sheets the modelling error.
whose rate is independent of the frequency. This will be illustrated by numerical experiments for straight and circular sheet. In the second part the calculation of the photonic crystal bandstructure is studied. Photonic crystals are periodic dielectric material, a structure which has high influence on the propagation of light. We are interested on the related parametric eigenvalue problem where the dispersion curves are the functions of the eigenvalues in dependence of the parameter. Based on the Fredholm theory we explicit formulas for the first and higher derivatives of the dispersion curves in terms of eigenvalue and eigenfunction.
order description of the band structure based on Taylor expansions.
