On asymptotic scales of independently stopped random sums

We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is assumed to be independent of the underlying process, which is a random walk. The main result enables one to identify whether the asymptotic behaviour of a stopped sum is dominated by the increment, or the stopping variable. As a consequence of this result, new sufficient conditions for the moment determinacy of compounded sums are obtained.Comment: 22 pages, 2 figure

Camelina success story

Camelina sativa is an ancient oilseed crop, which has been cultivated in Europe during the iron and bronze ages. The seeds contain about 40 % oil. Camelina oil has an excellent fatty acid composition: 40 % omega-3 fatty acids and 16 % omega-6 fatty acids

Overlearning in marginal distribution-based ICA: analysis and solutions

The present paper is written as a word of caution, with users of independent component analysis (ICA) in mind, to overlearning phenomena that are often observed.\\ We consider two types of overlearning, typical to high-order statistics based ICA. These algorithms can be seen to maximise the negentropy of the source estimates. The first kind of overlearning results in the generation of spike-like signals, if there are not enough samples in the data or there is a considerable amount of noise present. It is argued that, if the data has power spectrum characterised by $1/f$ curve, we face a more severe problem, which cannot be solved inside the strict ICA model. This overlearning is better characterised by bumps instead of spikes. Both overlearning types are demonstrated in the case of artificial signals as well as magnetoencephalograms (MEG). Several methods are suggested to circumvent both types, either by making the estimation of the ICA model more robust or by including further modelling of the data

Regional Externalities in the Dynamic System of Three Regions

This study presents theoretical models of the role of externalities across two and three dimensional regional economy. Two decades ago Krugman (1981) developed a model of uneven regional development. He showed that initial discrepancy in capital-labour ratios of the two adjacent, competing regions will cumulate over time, and will inevitably lead to the division into the capital-rich and capital-poor regions. Kubo (1995) presented an extension to Krugman?s model by incorporating not only scale economies within the regions but also regional externalities across regions. His model provided an explanation for different regional development patterns: uneven, joint and the mix of these two. In this study Kubo?s analysis is extended to study the dynamic properties of the development of the three regions instead of two regions. We characterise dynamics and the stability of steady states in the three-region model. In particular, we show under what conditions steady state is unique, and if there can be multiple steady states. We show that condition for even regional development in Kubo?s model, i.e. regional externalities are stronger than scale economies in each regions, is necessary, but not a sufficient condition for even regional development in a case of three region. Our study sheds light on e.g. the regional development in Northern Finland. A few years ago the idea of the regional network of Northern Finland was launched. That idea was meant to spread the economic growth of the city of Oulu - technologically advanced core region - to smaller peripheral areas. Models of this study offer potentially interesting frameworks to analyse different regional development patterns. Furthermore, our model can be used to analyse, how the domination of core region affects the growth of peripheral regions and what kind of regional policy should be implemented to promote economic growth in the periphery. Keywords: Scale economies, regional externalities, regional development JEL classification: C61, R12