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The simulation of fabrication processes for microelectronic devices is one possible application of the methods studied in the thesis. eration is crucial in the development of semiconductor devices. In the first part of the talk the model is introduced and the qualitative properties of the equations will be summarized. Next, a discretization in space and time of the system is derived which preserves the physical properties of the continuous problem. The application of the numerical method to a CCD sensor illustrates the working principle of many electronic cameras. The talk gives an short overview of the results of my thesis. Then a Voronoi finite volume method in space and implicit Euler in time discretization is introduced.
Next, the new analytical results concerning the discretized problem obtained in the thesis will be summarized. numerical example will demonstrate the stability of the method. WIAS Berlin Mittwoch, 11. Mean field games are part of large population stochastic control. The purpose of the talk is to make rigorous the notion of master equation. The master equation is a PDE built on the space of measures.
It encapsulates all the necessary information to describe an equilibrium. To conclude, I will show how to use the master equation to justify the passage from a finite population to an infinite one. Universität zu Berlin Technische Universität Berlin Mittwoch, 11. dimensional ODE which exhibits explosion in finite time. in the sense that for each initial condition there is almost surely no explosion. Furthermore, the associated Markov process even admits an invariant probability measure. The question of interest is whether the noise also induces a stronger concept of stability, namely the existence of an attractor.
We give two examples which answer the question in different ways. Universität zu Berlin Technische Universität Berlin Mittwoch, 11. Universität zu Berlin Mittwoch, 11. WIAS Berlin Mittwoch, 11. Forschungsseminar Mathematische Statistik Prof. This paper introduces a model with regime switching, which is driven by an autoregressive latent factor correlated with the innovation to the observed time series. In our model, the mean or volatility process is switched between two regimes, depending upon whether the underlying autoregressive latent factor takes values above or below some threshold level. If the latent factor becomes exogenous, our model reduces to the conventional markov switching model, and therefore, our model may be regarded as an extended markov switching model allowing for endogeneity in regime switching. Our model is estimated by the maximum likelihood method using a newly developed modified markov switching filter.
For both mean and volatility models that are frequently analyzed in markov switching framework, we demonstrate that the presence of endogeneity in regime switching is indeed strong and ubiquitous. Universität zu Berlin Universität Potsdam Dienstag, 10. level Monte Carlo approach is a powerful variance reduction technique, which is applied, in particular, in the context of stochastic differential equations. valued functional on the path space, in this talk we discuss how to approximate its distribution function or density on a compact interval in this talk. level Monte Carlo, and we establish upper bounds for the error of suitable algorithms.
which is a process engineering technique for the separation of nanoparticles. WIAS Berlin Donnerstag, 05. Forschungsseminar Mathematische Modelle der Photonik PD Dr. Universität zu Berlin WIAS Berlin Mittwoch, 04. Forschungsseminar Mathematische Statistik Dr. What drives the Yield curve? The tests are based on nonparametric estimators of the model developed under the null of the Markov hypothesis and under the alternative, respectively.
erent from each other. The tests do not rely on particular functional form assumptions and so are able to disentangle the Markov hypothesis from functional form hypotheses. usion such a structure is frequently considered in the term structure literature. In an empirical application, we implement estimators and tests on US term structure data.
Universität zu Berlin Universität Potsdam Dienstag, 03. Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics Dr. The first goal of the talk is to familiarize listeners with recent results by Olivier Devolder, Francois Glineur, and Yurii Nesterov concerning convex optimization problems with inexact oracle. Two levels of inexactness are considered: a deterministic one, which means that the function is convex and approximately smooth and stochastic one, which means that we are alowed to calculate only stochastic approximation of the function value and gradient. accumulate the error of the oracle. On the contrary the fast gradient method has faster convergence rate but linearly accumulates the oracle error. This method allows to play with tradeoff between the speed and error accumulation depending on the problem parameters.
Joint work with Alexander Gasnikov. WIAS Berlin Dienstag, 03. Seminar Nichtlineare Optimierung und Inverse Probleme Dr. WIAS Berlin Mittwoch, 28. with various applications in economics and finances. Universität zu Berlin Technische Universität Berlin Mittwoch, 28. We consider one dimensional diffusion process observed at regularly sampled time points, with fixed time between observations. We give example of optimal estimator of diffusion coefficients, based on spectral properties of the transition semi group.
We investigate the behavior of this estimator when time between observations decreases to zero and discuss its effectiveness in high frequency regime. Universität zu Berlin Technische Universität Berlin Mittwoch, 28. Universität zu Berlin Mittwoch, 28. Forschungsseminar Mathematische Statistik Dr. of kernel estimators and provides optimal results in this setting. likelihood estimate and in statistical learning with noisy data such as in quantile and moment estimation, in discriminant analysis and in clustering. driven procedures selecting isotropic bandwidths, however, none of them allows anisotropic bandwidth selection. driven selection of anisotropic bandwidths in the large setting of empirical risk minimization.
in noisy clustering as well as adaptive minimax results for pointwise and global estimation in nonparametric regression. Universität zu Berlin Universität Potsdam Dienstag, 27. Oberseminar Nonlinear Dynamics Prof. WIAS Berlin Freie Universität Berlin Dienstag, 27. Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics Dr. Image registration is an essential task in almost all areas involving imaging techniques. The goal of image registration is to find geometrical correspondences between two or more images. or introduce prior knowledge about the application in mind. This talk presents a nonlinear regularization functional based on the theory of hyperelastic materials, which overcomes limitations of the most commonly used linear elastic model.
one correspondences between the images, which is a key concern in most applications. The focus of this talk is on accurate and fast numerical methods for solving hyperelastic image registration problems. WIAS Berlin Dienstag, 27. Seminar Numerische Mathematik Prof. sup deficiency associated to a given pair of finite element spaces. Then, I will present the application of this idea to two different problems.
Mindlin plate problem, and in the second part I will briefly present a stabilised finite element method for a fictitious domain formulation. WIAS Berlin Dienstag, 27. Seminar Nichtlineare Optimierung und Inverse Probleme Prof. WIAS Berlin Donnerstag, 22. Seminar Numerische Mathematik Dr. The aim of the talk is to show the connections of some analytic and stochastic concepts. All is presented from an analytical point of view.
We give an overview of some evolution equations describing deterministic and stochastic problems in classical physics. WIAS Berlin Mittwoch, 21. One of the motivations of our program was to develop understanding of the interplay between the nonlinear and nonlocal components in evolution equation driven by the infinitesimal generators of stochastic processes with jumps, such as Levy processes and flights. Universität zu Berlin Technische Universität Berlin WIAS Berlin 21. Universität zu Berlin Technische Universität Berlin WIAS Berlin Dienstag, 20. Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics Dr Th. WIAS Berlin Dienstag, 20. Seminar Nichtlineare Optimierung und Inverse Probleme Prof. liquid phase transitions in the context of welding processes, material accumulation by melting, and similar.
The model includes heat transfer, melting and solidification, and free surface melt flow. Special care is needed expecially where different free boundaries meet. WIAS Berlin Dienstag, 20. Sivashinsky equation with periodic boundary value condition is considered. homogeneous t periodic solutions.
These manifolds can be stable or unstable but all solutions of these manifolds are always unstable.