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Kolmogorov Equation (kolmogorov + equation)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

Probabilistic yielding and cyclic behavior of geomaterials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2010
Kallol Sett
Abstract In this paper, the novel concept of probabilistic yielding is used for 1-D cyclic simulation of the constitutive behavior of geomaterials. Fokker,Planck,Kolmogorov equation-based probabilistic elastic,plastic constitutive framework is applied for obtaining the complete probabilistic (probability density function) material response. Both perfectly plastic and hardening-type material models are considered. It is shown that when uncertainties in material parameters are taken into consideration, even the simple, elastic-perfectly plastic model captures some of the important features of geomaterial behavior, for example, modulus reduction with cyclic strain, which, deterministically, is only possible with more advanced constitutive models. Furthermore, it is also shown that the use of isotropic and kinematic hardening rules does not significantly improve the probabilistic material response. Copyright © 2010 John Wiley & Sons, Ltd. [source]

On the asymptotic positivity of solutions for the extended Fisher,Kolmogorov equation with nonlinear diffusion

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2002
M. V. Bartuccelli
Abstract The objective of this paper aims to prove positivity of solutions for a semilinear dissipative partial differential equation with non-linear diffusion. The equation is a generalized model of the well-known Fisher,Kolmogorov equation and represents a class of dissipative partial differential equations containing differential operators of higher order than the Laplacian. It arises in a variety of meaningful physical situations including gas flows, diffusion of an electron,ion plasma and the dynamics of biological populations whose mobility is density dependent. In all these situations, the solutions of the equation must be positive functions. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009
R. Gutiérrez
Abstract In the present study, we treat the stochastic homogeneous Gompertz diffusion process (SHGDP) by the approach of the Kolmogorov equation. Firstly, using a transformation in diffusion processes, we show that the probability transition density function of this process has a lognormal time-dependent distribution, from which the trend and conditional trend functions and the stationary distribution are obtained. Second, the maximum likelihood approach is adapted to the problem of parameters estimation in the drift and the diffusion coefficient using discrete sampling of the process, then the approximated asymptotic confidence intervals of the parameter are obtained. Later, we obtain the corresponding inference of the stochastic homogeneous lognormal diffusion process as limit from the inference of SHGDP when the deceleration factor tends to zero. A statistical methodology, based on the above results, is proposed for trend analysis. Such a methodology is applied to modelling and forecasting vehicle stocks. Finally, an application is given to illustrate the methodology presented using real data, concretely the total vehicle stocks in Spain. Copyright © 2008 John Wiley & Sons, Ltd. [source]