Limit theorems for solutions of stochastic differential equation problems

In this paper linear differential equations with random processes as coefficients and as inhomogeneous term are regarded. Limit theorems are proved for the solutions of these equations if the random processes are weakly correlated processes

The spectrum of the random environment and localization of noise

We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized.Comment: 18 pages, 1 figur

Untersuchung der Mikrowellenemission eines Strahl-Plasma-Experiments

with 59 refs.SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Results of Statistical Data Analysis of Random Road Profiles

The investigation of road vehicle dynamics has to take into account the influence of road irregularities. To do this various road profiles have been surveyed. Samples of road profile heights can be used as input of vehicle dynamics simulation or to fit appropriate random road models to the data. For supporting this modeling part the paper presents some statistical characteristics of a number of road profile samples. 1 Introduction The paper reports the results of a statistical data analysis of some samples of measured road profile heights. First, there are six so-called IR6 samples, which have been used for the investigation of vehicle dynamics by a research group of the department of road vehicles at TU Budapest. Second, two samples used by a research group of the department of mathematics of the former TH Zwickau, are analysed. One of these two samples has been used to fit a model to the data. Monte-Carlo simulations based on this model are the source of a third group of samples. Th..

On the Analytic Representation of the Correlation Function of Linear Random Vibration Systems

This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result analytic expressions of some integrals involved in the expansion terms are derived. 1 Introduction Mathematical modeling of real-world vibration systems (e. g. vehicles moving on a rough guideway, rotating generator shafts excited by random fluctuations of the generator torque) results in a system of ordinary differential equations (ODE) containing random parameters. For a linear system with n degrees of freedom (DOF) and a random external excitation we get A p +B p + Cp = f(t; !) (1) with the initial conditions ..

Limit Theorems for Functionals of the Derivatives of Weakly Correlated Functions and Applications to Random Boundary Value Problems

In this paper a random Sturm-boundary-value problem is considered. Thereby, the random coefficients belong to the class of weakly correlated functions, which can be characterized as functions "without distance effect". There exist various solution methods for this problem in the literature. The aim is to compare these methods and to examine their compatibility. For that, it is useful to consider limit theorems for integral functionals of the derivatives of weakly correlated functions. 1 Introduction Let us consider the random boundary value problem L(!)u = g(x; !) (1) U i [u] = 0; i = 1; 2; : : : ; 2n; 0 x 1; where the operator L(!) is given by L(!)u := n X i=0 (\Gamma1) i h f i (x; !)u (i) i (i) and U i by U i [u] = 2n\Gamma1 X j=0 i ff ij u (j) (0) + fi ij u (j) (1) j = 0; i = 1; 2; : : : ; 2n: Let ( \Delta ; \Delta ) denote the scalar product of L 2 (0; 1). The (non-random) boundary conditions U i (i = 1; 2; : : : ; 2n) have to be constituted so that (L..