Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum

In this paper, we revisit the classical results on the generalized St. Petersburg sums. We determine the limit distribution of the St. Petersburg sum conditioning on its maximum, and we analyze how the limit depends on the value of the maximum. As an application, we obtain an infinite sum representation of the distribution function of the possible semistable limits. In the representation, each term corresponds to a given maximum, in particular this result explains that the semistable behavior is caused by the typical values of the maximum.Comment: Published at http://dx.doi.org/10.3150/14-BEJ685 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The accuracy of merging approximation in generalized St. Petersburg games

Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games, extending the short expansions due to Cs\"org\H{o}, S., Merging asymptotic expansions in generalized St. Petersburg games, \textit{Acta Sci. Math. (Szeged)} \textbf{73} 297--331, 2007. These expansions are given in terms of suitably chosen members from the classes of subsequential semistable infinitely divisible asymptotic distribution functions and certain derivatives of these functions. The length of the expansion depends upon the tail parameter. Both uniform and nonuniform bounds are presented.Comment: 30 pages long version (to appear in Journal of Theoretical Probability); some corrected typo

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

Post-Socialist Transformation of Central and Eastern Europe at the Turn of the Century: Regional Development and Economic Inequality

The evolution of socio-economic systems is non-linear, it includes both the periods of smooth changes and subsequent abrupt transformational leaps. The overall structure of new prospects opens as early as at the stage of emerging evolutionary processes, and their forecast requires to analyze the historical premises and risks that are closely associated with the change of public attitudes. With the collapse of the Soviet Union, the newly independent states went through a transformational and evolutionary development stage that led them from a regional economy (since they actually had been the regions) to the national economy, while the countries in Central and Eastern Europe experienced a dramatic drift towards the European Union. This paper examines the results of almost 25-year-long transformation of these countries. The new states that emerged following the collapse of the Soviet Union went through three types of transformation. First, there were transformations on the ideological level. The transformations of the second type were purely economic. The third type can be described as institutional (including structural and financial) transformation. It has been demonstrated that one of the important reasons for modest economic performance in the post-Soviet space was the fact that the new states ignored and did not use the principles of regional policy and regional modernization in their state-building practice. A characteristic feature in the socio-economic evolution of Eastern Europe after 1990 was a sharply emphasized process of stratification and social differentiation occurring against the backdrop of insufficiently strong middle class and the polarization of income levels in different regions. The growing polarization of income levels in different regions represents the dominant trend of rising economic inequality.This research has been conducted with the support of the Russian Science Foundation (the Grant No. 14–28–00065) "Structural and Cyclical Paradigm of Economic and Technological Renewal of Macro-Social Systems (World and Russia in the First Half of the 21st century).

Alternative proof and interpretations for a recent state-dependent importance sampling scheme

Recently, a state-dependent change of measure for simulating overflows in the two-node tandem queue was proposed by Dupuis et al. (Ann. Appl. Probab. 17(4):1306–1346, 2007), together with a proof of its asymptotic optimality. In the present paper, we present an alternative, shorter and simpler proof. As a side result, we obtain interpretations for several of the quantities involved in the change of measure in terms of likelihood ratios

The Role of the City in Fostering Intergroup Communication in a Multicultural Environment: Saint-Petersburg’s Case

In this paper two aspects of the issue will be discussed. First, there is the role of authorities, NGOs in forming the multicultural environment in the city with cultural diversity. Second, the city as social context, the images and myths of the city determine discourse on multiculturalism and influence the cross-cultural communication in the city. After describing historically shaped images of the city, employment of city’s myths and symbols in discourse and policy of multiculturalism, and role of city’s institutions in fostering inter-group communication, this paper will discuss the inclusive culture of the city, shaped by the networking interaction, which blurs the distinction between «insiders» and «outsiders». Here the trends of (post)modern inter/trans-national relations will be extrapolated on the trans-cultural interaction in the multicultural city, taking into consideration that network interactions build up not between the territories, but in the space, where logic of borders overcomes.Multicultural, Identity, Image, Myth, Discourse, We-groups, Inclusive networks, Inclusive culture, Transnational interaction, Transnational civil society