Veranstaltungen

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Mittwoch, 21.11.2018, 10:00 Uhr (WIAS-406)
Forschungsseminar Mathematische Statistik
Prof. M. Bibinger, Universität Marburg:
Statistical analysis of path properties of volatility
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
In this talk, we review recent contributions on statistical theory to infer path properties of volatility. The interest is in the latent volatility of an It^o semimartingale, the latter being discretely observed over a fixed time horizon. We consider tests to discriminate continuous paths from paths with volatility jumps. Both a local test for jumps at speciied times and a global test for jumps over the whole observation interval are discussed. We establish consistency and optimality properties under infill asymptotics, also for observations with additional additive noise. Recently, there is high interest in the smoothness regularity of the volatility process as confl icting models are proposed in the literature. To address this point, we consider inference on the Hurst exponent of fractional stochastic volatility processes. Even though the regularity of the volatility determines optimal spot volatility estimation methods, forecasting techniques and the volatility persistence, identifiability is an unsolved question in high-frequency statistics. We discuss a first approach which can reveal if path properties are stable over time or changing. Eventually, we discuss some recent considerations and conjectures on this open question. The related easier problem of inference on the Hurst exponent from direct discrete observations of a fractional Brownian motion is also visited.

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Mittwoch, 21.11.2018, 10:45 Uhr (WIAS-HVP-3.13)
Seminar Interacting Random Systems
W. Sun, TU Berlin:
On the asymptotic distribution of nucleation times of polymerization processes
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstrakt
Experiments have shown that there is a sharp phase transition in polymerization: it takes long time to have small amount of stable polymers and once some amount of stable polymers appear, very quickly all particles are polymerized. Moreover, the lag time usually have a very high variance. We propose a growth-fragmentation model with a critical mass to explain these phenomenon. Particles having a mass less than this critical mass are unstable -- they are fragmented much more quicker than the larger particles. A scaling approach is used, by taking the initial total mass N as a scaling parameter and assuming that the ratio of the unstable fragmentation rates to stable fragmentation rates are of order Phi(N), which is a non-decreasing function of N. We study the time evolution of this infinite dimension process under a certain class of fragmentation distributions. We show that 1) with a proper scaling parameter, the time (T) spent for the stable polymers that generating from small particles is asymptotically exponential distributed; 2) the time for the growth of stable particles has a much smaller order than T. The exponential distribution explains the high variance and the different time scales explain the sharp phase transition. These results are proved via stochastic calculus, estimations for occupation measures on different time scales, some coupling techniques and branching processes. It is a joint work with Philippe Robert.

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Forschungsgruppenseminar Interacting Random System

Veranstalter
WIAS Berlin
Mittwoch, 28.11.2018, 10:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. M. Schienle, Karlsruher Institut für Technologie:
Determination of vector error correction models for different types of high-dimensionality
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We provide a shrinkage type methodology which allows for simultaneous model selection and estimation of vector error correction models (VECM) when the dimension is large and can increase with sample size. Model determination is treated as a joint selection problem of cointegrating rank and autoregressive lags under respective practically valid sparsity assumptions. We show consistency of the selection mechanism by the resulting Lasso-VECM estimator under very general assumptions on dimension, rank and error terms. Moreover, with computational complexity of a linear programming problem only, the procedure remains computationally tractable in high dimensions. For the subcase of finite dimensions, we can modify and tailor the procedure with elementwise selection consistency. For ultra-high dimensions we suggest a completely diferent pre-screening approach. We demonstrate the effectiveness of the proposed techniques in simulations and an empirical application to recent CDS data after the financial crisis.

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Forschungsseminar “Mathematische Statistik”

Veranstalter
Universität Potsdam
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 28.11.2018, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. P.-É. Druet, WIAS:
Analysis of mass transfer, Navier--Stokes equations for multicomponent fluids subject to a volume constraint
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 29.11.2018, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. J.H.M. ten Thije Boonkkamp, Eindhoven University of Technology, Niederlande:
Flux vector approximation schemes for systems of conservation laws
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Conservation laws in continuum physics are often coupled, for example the continuity equations for a reacting gas mixture or a plasma are coupled through multi-species diffusion and a complicated reaction mechanism. For space discretisation of these equations we employ the finite volume method. The purpose of this talk is to present novel flux vector approximation schemes that incorporate this coupling in the discretisation. More specifically, we consider as model problems linear advection-diffusion systems with a nonlinear source and linear diffusion-reaction systems, also with a nonlinear source. The new flux approximation schemes are inspired by the complete flux scheme for scalar equations, see [1]. An extension to systems of equations is presented in [2]. The basic idea is to compute the numerical flux vector at a cell interface from a local inhomogeneous ODE-system, thus including the nonlinear source. As a consequence, the numerical flux vector is the superposition of a homogeneous flux, corresponding to the homogeneous ODE-system, and an inhomogeneous flux, taking into account the effect of the nonlinear source. The homogeneous ODE-system is either an advection-diffusion system or a diffusion-reaction system. In the first case, the homogeneous flux contains only real-valued exponentials, on the other hand, in the second case, also complex-valued components are possible, generating oscillatory solutions. The inclusion of the inhomogeneous flux makes that all schemes display second order convergence, uniformly in all parameters (Peclet and Damköhler numbers). The performance of the novel schemes is demonstrated for several test cases, moreover, we investigate several limiting cases.
References
[1] J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen, “The finite volume-complete flux scheme for advection-diffusion-reaction equations”, J. Sci. Comput., 46, 47--70, (2011).
[2] J.H.M. ten Thije Boonkkamp, J. van Dijk, L. Liu and K.S.C. Peerenboom, “Extension of the complete flux scheme to systems of comservation laws”, J. Sci. Comput., 53, 552--568, (2012).

Veranstalter
WIAS Berlin
Mittwoch, 05.12.2018, 11:30 Uhr (WIAS-HVP-3.13)
Seminar Interacting Random Systems
Prof. Dr. S. Popov, University of Campinas --- UNICAMP, Brasilien:
Two-dimensional random interlacements, conditional SRW, and the cryptocurrencies
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstrakt
Serguei Popov will briefly describe his recent research topics mentioned in the title.

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin
Dienstag, 11.12.2018, 10:15 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. J. Machalová, Palacky University Olomouc, Tschechische Republik:
Contact problem solution for nonlinear beam and foundation by CVM
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Veranstalter
WIAS Berlin
Dienstag, 11.12.2018, 13:30 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. W. Dreyer, WIAS Berlin:
Kinetic theory of incompressible non-newtonian fluids
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We consider a non-newtonian fluid consisting of a newtonian solvent and polymer molecules as solute. The kinetic theory models the polymer molecules as dumbbells and compiles dynamical equations that embody internal dumbbell interactions and interactions of the dumbbell with the surrounding fluid via its velocity gradient. The dynamical equations imply a generalized Fokker-Planck equation for a distribution function of the system of polymer molecules. Then the Fokker--Planck equation is used to derive macroscopic evolution equations for certain mean values. For given velocity gradient of the fluid, three evolution equations are needed to end up with a closed equation system for the polymer molecules. The corresponding three thermodynamic variables are the number density, the mean squared end-to end distance of a polymer molecule and the polymer stress. Finally we prove an H-theorem and solve the subtle problem of thermodynamic consistency.

Veranstalter
WIAS Berlin
Mittwoch, 12.12.2018, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. J. Rehberg, WIAS Berlin:
L bounds for the Neumann problem
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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

Veranstalter
WIAS Berlin
Humboldt-Universität zu Berlin