We consider a general class of discrete-space linear partial dynamic equations. The basic properties of solutions are provided (existence and uniqueness, sign preservation, maximum principle). Above all, we derive the following main results: first, we prove that the solutions depend continuously on the choice of the time scale. Second, we show that, under certain conditions, the solutions descr...

We address in this paper the challenge of solving a nonhomogeneous infinite horizon Markov Decision Process (MDP) problem. More precisely, we seek an algorithm that, when given a finite subset of the problem’s potentially infinite data set, delivers an optimal first period policy. Such an algorithm can thus recursively generate within a rolling horizon procedure an infinite horizon optimal solu...

Precipitation has a dominant role in agriculture, and regular rain pattern is usually vital to agriculture; excessive or inadequate rainfall can be harmful. In this paper, an agricultural drought index utilized study the periods analyze them with their intensities at various locations. Some nonhomogeneous Poisson models are also used calculate probability of droughts (number times occurred) tim...

Simplifying assumptions made in various tree reconstruction methods--notably rate constancy among nucleotide sites, homogeneity, and stationarity of the substitutional processes--are clearly violated when nucleotide sequences are used to infer distant relationships. Use of tree reconstruction methods based on such oversimplified assumptions can lead to misleading results, as pointed out by prev...

∗Department of Mathematics, Technion-Israel Institute of Technology ∗∗Vologda State Pedagogical University and Vologda Scientific Coordinate Centre of CEMI RAS, Vologda, Russia email: [email protected] Received October 14, 2002 Evaluation of the rate of convergence of stochastic models, as time t → ∞, has been a subject of investigation by generations of probabilists. During the last two de...

We consider finite-state time-nonhomogeneous Markov chains whose transition matrix at time n is I + G/nζ where G is a “generator” matrix, that is G(i, j) > 0 for i, j distinct, and G(i, i) = − ∑ k 6=iG(i, k), and ζ > 0 is a strength parameter. In these chains, as time grows, the positions are less and less likely to change, and so form simple models of age-dependent time-reinforcing schemes. Th...