Markov chains have been frequently used to characterize uncertainty in many real-world problems. Quite often, these Markov chains can be decomposed into a vector consisting of fast and slow components; these components are coupled through weak and strong interactions. The main goal of this work is to study the structural properties of such Markov chains. Under mild conditions, it is proved that the underlying Markov chain can be approximated in the weak topology of L2 by an aggregated process. Moreover, the aggregated process is shown to converge in distribution to a Markov chain as the rate of fast transitions tends to infinity. Under an additional Lipschitz condition, error bounds of the approximation sequences are obtained. 相似文献
With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau–Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives. 相似文献
Using the electric approach, we derive exact and asymptotic closed form formulas for hitting times in symmetric cases of the Moran's genetics model. 相似文献
We consider several applications of two state, finite action, infinite horizon, discrete-time Markov decision processes with partial observations, for two special cases of observation quality, and show that in each of these cases the optimal cost function is piecewise linear. This in turn allows us to obtain either explicit formulas or simplified algorithms to compute the optimal cost function and the associated optimal control policy. Several examples are presented.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-86-0029, in part by the National Science Foundation under Grant ECS-8617860, in part by the Advanced Technology Program of the State of Texas, and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-86-C-0045. 相似文献
The influence of 200 keV Ar-ion irradiation on the interlayer coupling in the Fe/Cr multilayer system exhibiting the giant magnetoresistance effect (GMR) is studied by conversion electron Mössbauer spectroscopy (CEMS), VSM hysteresis loops, magnetoresistivity and electric resistivity measurements and supplemented by the small-angle X-ray diffraction (SAXRD). The increase of Ar ion dose causes an increase of interface roughness, as evidenced by the increase of the Fe step-sites detected by CEMS as a result of which the GMR gradually decreases and vanishes at doses exceeding 1×1014 Ar/cm2. A degradation of GMR with increasing Ar-ion dose is related to the formation of pinholes between Fe layers and the decrease of the antiferromagnetically coupled fraction.
Using the defining matrices of A_1 in classical algebras A_n, B_n, C_n and D_n, deduce the embedding indices of the physical A_1 algebra in classical algebras, The Ginocchio so (8) model is as an example. 相似文献