Strategic measures in optimal control problems for stochastic sequences

Controlled discrete–time stochastic processes axe studied using the convex–analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.     

Pseudoprocesses on a circle and related Poisson kernels

Pseudoprocesses, constructed by means of the solutions of higher-order heat-type equations, have been developed by several authors and many related functionals have been analysed by applying the Feynman–Kac functional or by means of the Spitzer identity. We here examine pseudoprocesses wrapped up on circles and derive their explicit signed density measures. By composing the circular pseudoprocesses with positively skewed stable processes, we arrive at genuine circular processes whose distribution is obtained in the form of Poisson kernels. The distribution of circular even-order pseudoprocesses is similar to the Von Mises (or Fisher) circular normal law and to the wrapped up law of Brownian motion. Time-fractional and space-fractional equations related to processes and pseudoprocesses on the unit radius circumference are introduced and analysed.     

Stable subsets of modules and the existence of a unit in associative rings

We obtain criteria for the existence of a (left) unit in rings (arbitrary, Artinian, Noetherian, prime, and so on) that are based on the systematic study of properties of stable subsets of modules and their stabilizers that generalize the technique of idempotents. We study a class of quasiunitary rings that is a natural extension of classes of rings with unit and of von Neumann (weakly) regular rings, which inherits may properties of these classes. Some quasiunitary radicals of arbitrary rings are constructed, and the size of these radicals “measures the probability” of the existence of a unit. Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 596–611, April, 1997. Translated by A. I. Shtern     

Competitive exclusion and coexistence in a Leslie–Gower competition model with Allee effects

The classical competitive exclusion principle states that two populations competing for a limited resource cannot coexist, one of the populations will drive the other to extinction. We prove in this work that when one population is subject to Allee effects, then for certain parameter regimes both competing populations may either coexist or one population may drive the other to extinction depending on initial conditions.     

Multiple attractors in a Leslie–Gower competition system with Allee effects

We investigate asymptotic dynamics of the classical Leslie–Gower competition model when both competing populations are subject to Allee effects. The system may possess four interior steady states. It is proved that for certain parameter regimes both competing populations may either go extinct, coexist or one population drives the other population to extinction depending on initial conditions.     

关于微分方程解的一致非常稳定性与一致距离有界性

讨论了一般非自治方程解的一致非常稳定性与一致距离有界性.     

Harnack’s Inequality for Stable Lévy Processes

We prove Harnacks inequality for harmonic functions of a symmetric stable Lévy process on R^d without the assumption that the density function of its Lévy measure is locally bounded from below. Mathematics Subject Classifications (2000) Primary 60J45, 31C05; Secondary 60G51.Research partially supported by KBN (2P03A 041 22) and RTN (HPRN-CT-2001-00273-HARP).     

Divide and conquer algorithms for computing the eigendecomposition of symmetric diagonal-plus-semiseparable matrices

Three fast and stable divide and conquer algorithms to compute the eigendecomposition of symmetric diagonal-plus-semiseparable matrices are considered. AMS subject classification 15A18, 15A23, 65F15The research of the second and the third author was supported by the Research Council K.U. Leuven, to13.25cmproject OT/00/16 (SLAP: Structured Linear Algebra Package), by the Fund for Scientific Research –