Kernel estimates for nonautonomous Kolmogorov equations with potential term

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term

Construction of Lp\mathcal L^p-strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions

We provide a general construction scheme for $\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated semigroup and resolvents of kernels having the $\mathcal L^p$-strong Feller property. They allow us to construct a process which solves the corresponding martingale problem for all starting points from a known set, namely the set where the regularity assumptions hold. We apply this result to construct elliptic diffusions having locally Lipschitz matrix coefficients and singular drifts on general open sets with absorption at the boundary. In this application elliptic regularity results imply the desired regularity assumptions

MULTIVARIATE MODEL OF ANALYSIS AND ASSESSMENT OF THE COMPETITIVENESS OF SOCIO-ECONOMIC SYSTEMS

A multifactor mathematical model for analyzing and evaluating the competitiveness of socio-economic systems has been developed. A review of the definitions of the concept of competitiveness used by various international institutions. According to the results of the review, the concepts of competitiveness, used in the present work, were formulated to identify the factors affecting it. A methodology for assessing competitiveness has been developed based on the analysis of the influence of four factors on it, characterized by 32 statistical indicators and corresponding significance indices. For the practical implementation of this technique developed a mathematical model. We analyzed the competitiveness of six regions of the Federation, representing six federal districts. The main directions of improving competitiveness for each subject of the Federation

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie