We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a Gaussian random field indexed by a measure space. We then show how existing theory for integration with respect to Gaussian processes indexed by [0, 1] can be ...

The study of precise large deviations for random sums is an important topic in insurance and finance. In this paper, we extend recent results of Tang (2006) and Liu (2009) to random sums in various situations. In particular, we establish a precise large deviation result for a nonstandard renewal risk model in which innovations, modelled as real-valued random variables, are negatively dependent ...

In this paper, we propose a novel approach for Fuzzy random-valued Optimization. The main idea behind our approach consists of taking advantage of interplays between fuzzy random variables and random sets in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. We consider a numerical example that shows the efficiency of the...

The concept of fuzzy random variable has been shown to be as a valuable model for handling fuzzy data in statistical problems. The theory of fuzzy-valued random elements provides a suitable formalization for the management of fuzzy data in the probabilistic setting. A concise overview of fuzzy random variables, focussed on the crucial aspects for data analysis, is presented. © 2006 Elsevier B.V...

We obtain asymptotic accuracy of the poissonisation in infinite occupancy scheme. All results are obtained for integer-valued random variables having a regularly varying distribution.

The sum. difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propos...