Preserving partial balance in continuous-time Markov chains

1987 ◽  
Vol 19 (2) ◽  
pp. 431-453 ◽  
Author(s):  
P. K. Pollett

Recently a number of authors have considered general procedures for coupling stochastic systems. If the individual components of a system, when considered in isolation, are found to possess the simplifying feature of either reversibility, quasireversibility or partial balance they can be coupled in such a way that the equilibrium analysis of the system is considerably simpler than one might expect in advance. In particular the system usually exhibits a product-form equilibrium distribution and this is often insensitive to the precise specification of the individual components. It is true, however, that certain kinds of components lose their simplifying feature if the specification of the coupling procedure changes. From a practical point of view it is important, therefore, to determine if, and then under what conditions, the revelant feature is preserved.In this paper we obtain conditions under which partial balance in a component is preserved and these often amount to the requirement that there exists a quantity which is unaffected by the internal workings of the component in question. We give particular attention to the components of a stratified clustering process as these most often suffer from loss of partial balance.

1987 ◽  
Vol 19 (02) ◽  
pp. 431-453 ◽  
Author(s):  
P. K. Pollett

Recently a number of authors have considered general procedures for coupling stochastic systems. If the individual components of a system, when considered in isolation, are found to possess the simplifying feature of either reversibility, quasireversibility or partial balance they can be coupled in such a way that the equilibrium analysis of the system is considerably simpler than one might expect in advance. In particular the system usually exhibits a product-form equilibrium distribution and this is often insensitive to the precise specification of the individual components. It is true, however, that certain kinds of components lose their simplifying feature if the specification of the coupling procedure changes. From a practical point of view it is important, therefore, to determine if, and then under what conditions, the revelant feature is preserved. In this paper we obtain conditions under which partial balance in a component is preserved and these often amount to the requirement that there exists a quantity which is unaffected by the internal workings of the component in question. We give particular attention to the components of a stratified clustering process as these most often suffer from loss of partial balance.


Author(s):  
Mokaedi V. Lekgari

In this study we first investigate the stability of subsampled discrete Markov chains through the use of the maximal coupling procedure. This is an extension of the available results on Markov chains and is realized through the analysis of the subsampled chain ΦΤn, where {Τn, nєZ+}is an increasing sequence of random stopping times. Then the similar results are realized for the stability of countable-state Continuous-time Markov processes by employing the skeleton-chain method.


2021 ◽  
pp. 107754632110280
Author(s):  
Xindong Si ◽  
Hongli Yang

Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation problem of stochastic systems considered in this article is also presented. Continuous-time stochastic linear systems and stochastic nonlinear systems are focused on, respectively. First, the condition of polyhedral invariance for stochastic systems is established by using the theory of positive invariant set and the principle of comparison. Second, the asymptotic stability conditions in the sense of expectation for two types of stochastic systems are established. Finally, finding the linear feedback controller model and corresponding algorithm of constrained regulation problem for two types of stochastic systems are also proposed by using the obtained condition. The presented model of the stochastic constrained regulation problem in this article is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Our approach establishes a connection between the stochastic constrained regulation problem and positively invariant set theory, as well as provides the possibility of using optimization methodology to find the solution of stochastic constrained regulation problem, which differs from other methods. Numerical examples illustrate the proposed method.


1972 ◽  
Vol 6 (3) ◽  
pp. 260-275 ◽  
Author(s):  
Baruch Berliner

E. Franckx [1] has established the distribution function of the largest individual claim of a portfolio. By assuming the number of claims to be Poisson distributed, H. Ammeter was able to develop the distribution function of the total loss excluding the largest individual claim [2] as well as the distribution function of the nth largest claim [3].Of course, the nth largest claim is dependent on the largest claim, second largest claim and so on, down to the (nth — 1) largest claim. If we assume the number of claims to be Poisson distributed and the amount of the individual claim to be Pareto distributed, the correlation between the mth largest and the nth largest claim can be expressed by an analytical formula which is susceptible to numerical computation.With this knowledge we shall be able to compute the variance of the sum of the n largest claims and moreover the correlation between the sum of the n largest claims and the total loss amount. Although an excess of loss reinsurance treaty and a treaty reinsuring the n largest claims are very different in their construction, this paper will show that from a practical point of view there exists a similarity between the two treaties. The correlation coefficient between the sum of the n largest claims and the sum of all claims exceeding a certain limit enables us to assess the degree of similarity.The correlation coefficient and thus the degree of similarity will prove to be high even in case of the reinsurance of only a small number of largest claims.Finally, the knowledge of the two first moments of the sum of the n largest claims allows us to compute the premium and the security or variance loading for the reinsurance of the n largest claims.


2019 ◽  
pp. 22-29
Author(s):  
Н. В. Фрадкіна

The purpose and tasks of the work are to analyze the contemporary Ukrainian mass culture in terms of its value and humanistic components, as well as the importance of cultural studies and Ukrainian studies in educational disciplines for the formation of a holistic worldview of modern youth.Analysis of research and publications. Scientists repeatedly turned to the problems of the role of spirituality in the formation of society and its culture. This problem is highlighted in the publications by O. Losev, V. Lytvyn, D. Likhachev, S. Avierintsev, M. Zakovych, I. Stepanenko and E. Kostyshyn.Experts see the main negative impact of mass culture on the quality approach, which determines mass culture through the market, because mass culture, from our point of view, is everything that is sold and used in mass demand.One of the most interesting studies on this issue was the work by the representatives of Frankfurt School M. Horkheimer and T. Adorno «Dialectics of Enlightenment» (1947), devoted to a detailed analysis of mass culture. Propaganda at all socio-cultural levels in the form is similar in both totalitarian and democratic countries. It is connected, according to the authors, with the direction of European enlightenment. The tendency to unify people is a manifestation of the influence of mass culture, from cinema to pop. Mass culture is a phenomenon whose existence is associated with commerce (accumulation in any form – this is the main feature of education), in general, the fact that it exists in this form is related to the direction of the history of civilization.Modern mass culture, with its externally attractive and easily assimilated ideas and symbols, appealing to the trends of modern fashion, becomes a standard of prestigious consumption, does not require intense reflection, allows you to relax, distract, not teach, but entertains, preaches hedonism as the main spiritual value. And as a consequence, there are socio-cultural risks: an active rejection of other people, which leads to the formation of indifference; cruelty as a character trait; increase of violent and mercenary crime; increase in the number of alcohol and drug addicts; anti-patriotism; indifference to the values of the family and as a result of social orphanhood and prostitution.Conclusions, perspectives of research. Thus, we can conclude that modern Ukrainian education is predominantly formed by the values of mass culture. Namely, according to the «Dialectic» by Horkheimer and Adorno, «semi-enlightenment becomes an objective spirit» of our modern society.It is concluded that only high-quality education can create the opposite of the onset of mass culture and the destruction of spirituality in our society. It is proved that only by realizing the importance of cultivating disciplines in the educational process and the spiritual upbringing of the nation, through educational reforms, humanitarian knowledge will gradually return to student audiences.Formation of youth occurs under the influence of social environment, culture, education and self-education. The optimal combination of these factors determines both the process of socialization itself and how successful it will be. In this context, one can see the leading role of education and upbringing. It turns out that the main task of modern education is to spread its influence on the development of spiritual culture of the individual, which eventually becomes a solid foundation for the formation of the individual. Such a subject requires both philosophical and humanitarian approaches in further integrated interdisciplinary research, since the availability of such research will provide the theoretical foundation for truly modern educational and personal development.


2020 ◽  
Vol 29 (4) ◽  
pp. 556-563
Author(s):  
Adam Burley

This is a personal and reflective piece written from a clinician's point of view on the influence that the developing awareness around the consequences of childhood adversity has had upon the discussions, thinking and practice across the areas in which they are working. It seeks to argue that the increased understanding and recognition of the potential impact of early adversity can not only enhance and deepen the understanding of an individual's difficulties, but can serve to inform how services respond in a way that takes account of this. It suggests that the research and literature on childhood adversity can offer a route map away from a model of mental health that focuses predominantly on the individual as the sole source of interest.


2020 ◽  

BACKGROUND: This paper deals with territorial distribution of the alcohol and drug addictions mortality at a level of the districts of the Slovak Republic. AIM: The aim of the paper is to explore the relations within the administrative territorial division of the Slovak Republic, that is, between the individual districts and hence, to reveal possibly hidden relation in alcohol and drug mortality. METHODS: The analysis is divided and executed into the two fragments – one belongs to the female sex, the other one belongs to the male sex. The standardised mortality rate is computed according to a sequence of the mathematical relations. The Euclidean distance is employed to compute the similarity within each pair of a whole data set. The cluster analysis examines is performed. The clusters are created by means of the mutual distances of the districts. The data is collected from the database of the Statistical Office of the Slovak Republic for all the districts of the Slovak Republic. The covered time span begins in the year 1996 and ends in the year 2015. RESULTS: The most substantial point is that the Slovak Republic possesses the regional disparities in a field of mortality expressed by the standardised mortality rate computed particularly for the diagnoses assigned to the alcohol and drug addictions at a considerably high level. However, the female sex and the male sex have the different outcome. The Bratislava III District keeps absolutely the most extreme position. It forms an own cluster for the both sexes too. The Topoľčany District bears a similar extreme position from a point of view of the male sex. All the Bratislava districts keep their mutual notable dissimilarity. Contrariwise, evaluation of a development of the regional disparities among the districts looks like notably heterogeneously. CONCLUSIONS: There are considerable regional discrepancies throughout the districts of the Slovak Republic. Hence, it is necessary to create a common platform how to proceed with the solution of this issue.


2008 ◽  
Vol 38 (01) ◽  
pp. 231-257 ◽  
Author(s):  
Holger Kraft ◽  
Mogens Steffensen

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.


1990 ◽  
Vol 22 (1-2) ◽  
pp. 347-352 ◽  
Author(s):  
C. Paffoni ◽  
B. Védry ◽  
M. Gousailles

The Paris Metropolitan area, which contains over eight million inhabitants, has a daily output of about 3 M cu.meters of wastewater, the purification of which is achieved by SIAAP (Paris Metropolitan Area Sewage Service) in both Achères and Valenton plants. The carbon pollution is eliminated from over 2 M cu.m/day at Achères. In order to improve the quality of output water, its tertiary nitrification in fixed-bed reactors has been contemplated. The BIOFOR (Degremont) and BIOCARBONE (OTV) processes could be tested in semi-industrial pilot reactors at the CRITER research center of SIAAP. At a reference temperature of 13°C, the removed load is approximately 0.5 kg N NH4/m3.day. From a practical point of view, it may be asserted that in such operating conditions as should be at the Achères plant, one cubic meter of filter can handle the tertiary nitification of one cubic meter of purified water per hour at an effluent temperature of 13°C.


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