scholarly journals Positive Dependence and Weak Convergence

2006 ◽  
Vol 43 (01) ◽  
pp. 48-59
Author(s):  
A. Colangelo ◽  
A. Müller ◽  
M. Scarsini

A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2 measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure is provided, and closure under weak convergence of the class of conditionally increasing measures is proved. As an application we investigate MTP2 properties of stationary distributions of Markov chains, which are of interest in actuarial science.

2006 ◽  
Vol 43 (1) ◽  
pp. 48-59 ◽  
Author(s):  
A. Colangelo ◽  
A. Müller ◽  
M. Scarsini

A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2 measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure is provided, and closure under weak convergence of the class of conditionally increasing measures is proved. As an application we investigate MTP2 properties of stationary distributions of Markov chains, which are of interest in actuarial science.


2021 ◽  
Author(s):  
Andrea Marin ◽  
Carla Piazza ◽  
Sabina Rossi

AbstractIn this paper, we deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the stationary performance indices of large stochastic models. The lumpability method is based on a state aggregation technique and applies to Markov chains exhibiting some structural regularity. Moreover, it allows one to efficiently compute the exact values of the stationary performance indices when the model is actually lumpable. The notion of quasi-lumpability is based on the idea that a Markov chain can be altered by relatively small perturbations of the transition rates in such a way that the new resulting Markov chain is lumpable. In this case, only upper and lower bounds on the performance indices can be derived. Here, we introduce a novel notion of quasi-lumpability, named proportional lumpability, which extends the original definition of lumpability but, differently from the general definition of quasi-lumpability, it allows one to derive exact stationary performance indices for the original process. We then introduce the notion of proportional bisimilarity for the terms of the performance process algebra PEPA. Proportional bisimilarity induces a proportional lumpability on the underlying continuous-time Markov chains. Finally, we prove some compositionality results and show the applicability of our theory through examples.


1979 ◽  
Vol 48 (1-4) ◽  
pp. 139-141

AbstractThe main subject of the debate was whether or not it is advisable to extend the concept of refugee beyond the present strict legal definitions and include more humanitarian concerns as suggested by Poul Hartling. On the one hand it was maintained in alia that — an extension of the international concept would create a discrepancy between the national concepts and the international concept — the concept of refugee applicable at the time of passing legislation concerning refugees still pertains — the quota-systems require strict adherence to legal definitions — the unsuccessful conference on territorial asylum proved the difficulty of adopting common norms of a broad humanitarian nature wrich is at the same time acceptable to governments - it was easier for the UNHCR in his pragmatic international work of a humanitarian administrative and social nature to adopt a wide concept, whereas the national refugee agencies whose problems is primarily that of issuing residence permits have to apply a more precise and narrow definition. Others took the view that — even in international law the concept of refugee is not totally static; in this respect it was mentioned that in spite of unmerous laws on refugees in Sweden, a precise definition has never been found - a liberal interpretation of existing written norms was called for rather than attempts to establish totally new definitions in a legally binding form - humanitarian concerns are not opposed to legal concepts; on the contrary, the legal concepts emerge from humanitarian and other political concerns — the definition in international law is to be considered a minimum norm. It was suggested that the refugee concept could be much wider in the field of assistance rather than in the field of protection. The dichotomy of having two refugee concepts, an international and a national come out as a practical problem when it comes to recognizing the refugee status. Theoretically, the dichotomy does not create serious problems, because the recognition is declaratory, not constitutive. In practical terms, there is a problem, however, because there is only one (effective) recognition of refugee status, the national recognition. It was noted that the High Commissioner often responded spontaneously to emergency situations involving wholely or in part groups of people falling beyond or on the verge of his mandate. The UN General Assembly, however, never failed to welcome such action thereby accepting a wider definition of UNCHR's mandate. The problems of de facto refugees were discussed. Reluctance was expressed towards extending the number of categories of refugees, e.g. by adding C and D categories to the A and B categories existing in the Nordic countries. It was preferable to extend the general definition of refugee in the manner of e.g. the Netherlands, Switzerland, or Sweden. A consequence of recognizing de facto refugees explicitly one way or the other was that the concept of de facto refugee would disappear. A common international definition which includes de facto refugees was called for. On the other hand, a warning was issued against adopting a very precise definition thereby creating new limits and new categories of people needing humanitarian assistance or protection but falling outside accepted categories. The problem of lacking international sanctions against countries which do not apply the international minimum standards was mentioned. It was pointed out, however, that the good offices and diplomatic initiatives of the High Commissioner often proved highly effective. Finally, a number of participants invited the High Commissioner to engage deeper into regional arrangements and to open a regional office in the Nordic countries.


2021 ◽  
Vol 58 (1) ◽  
pp. 177-196
Author(s):  
Servet Martínez

AbstractWe consider a strictly substochastic matrix or a stochastic matrix with absorbing states. By using quasi-stationary distributions we show that there is an associated canonical Markov chain that is built from the resurrected chain, the absorbing states, and the hitting times, together with a random walk on the absorbing states, which is necessary for achieving time stationarity. Based upon the 2-stringing representation of the resurrected chain, we supply a stationary representation of the killed and the absorbed chains. The entropies of these representations have a clear meaning when one identifies the probability measure of natural factors. The balance between the entropies of these representations and the entropy of the canonical chain serves to check the correctness of the whole construction.


Author(s):  
W. A. Shannon ◽  
M. A. Matlib

Numerous studies have dealt with the cytochemical localization of cytochrome oxidase via cytochrome c. More recent studies have dealt with indicating initial foci of this reaction by altering incubation pH (1) or postosmication procedure (2,3). The following study is an attempt to locate such foci by altering membrane permeability. It is thought that such alterations within the limits of maintaining morphological integrity of the membranes will ease the entry of exogenous substrates resulting in a much quicker oxidation and subsequently a more precise definition of the oxidative reaction.The diaminobenzidine (DAB) method of Seligman et al. (4) was used. Minced pieces of rat liver were incubated for 1 hr following toluene treatment (5,6). Experimental variations consisted of incubating fixed or unfixed tissues treated with toluene and unfixed tissues treated with toluene and subsequently fixed.


Author(s):  
Susan C. Graham

Culinary experiences have long been an important aspect of tourism. For many destinations, culinary offerings have become ubiquitous with the place – pasta in Italy, wine in the Loire- or Napa Valley, or curry in India. As tourists increasingly seek out authentic touristic experiences, including culinary experiences, the question arises regarding what constitutes an authentic culinary experience in a place. While authentic and authenticity are terms widely used in the tourism literature, a precise definition of what those terms mean and a method for identifying that which is authentic remains elusive. Research regarding authenticity in tourism suggests that locals occupy a ‘place of privilege’ with respect to determining the authenticity of a touristic experience because of their connection to and context in relation to the place. This paper examines the perspectives of Prince Edward Island (PEI) residents with respect to what constitutes an authentic culinary touristic experience in which visitors to Canada’s smallest province can partake and that provide those visitors with a glimpse of what life in PEI is or was really like, and provides a voice for an underrepresented group in the authenticity discourse. Results show that authentic culinary experiences transcend food, and encompass people, places, and experiences in ways that enrich touristic endeavours, and that locals understand and interpret authenticity in ways that both conform to and differ from existing scholarly work related to tourism authenticity, and span objective, existential, and constructive authenticity.


Author(s):  
Johannes Lindvall

This chapter introduces the problem of “reform capacity” (the ability of political decision-makers to adopt and implement policy changes that benefit society as a whole, by adjusting public policies to changing economic, social, and political circumstances). The chapter also reviews the long-standing discussion in political science about the relationship between political institutions and effective government. Furthermore, the chapter explains why the possibility of compensation matters greatly for the politics of reform; provides a precise definition of the concept of reform capacity; describes the book's general approach to this problem; and discusses the ethics of compensating losers from reform; and presents the book's methodological approach.


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