We give a comparison inequality that allows one to estimate the tail probabilities of sums of independent Banach space valued random variables in terms of those of independent identically distributed random variables. More precisely, let X1, . . . , Xn be independent Banach-valued random variables. Let I be a random variable independent of X1, . . . , Xn and uniformly distributed over {1, . . ....

Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of global quantities, in a direct or indirect way. This review discusses differe...

\7e have investigated the fluctuations of sums of random variables X.., Xp, ... . We have generalized previous results on the random variables H connected with this sequence, obtained new results on the validity of the Arc-sine Law for independent not identically distributed random variables, obtained a generalization of Spitzer's identity, and obtained a generalization of the equivalence princ...

In [9] we introduced a new framework for asymptotic probabilities. in which a r i-add~t~ve measure is defined on the sample space of all sequences A =< dl.d?. . d, > of finite models. where the uniberse of sf,, is { I . 2. ...n ) . In this framework we Investigated the strong 0-1 law for sentences. whlch states that each sentence either holds in d,, eventually almost surely or fails In d,, even...

We consider the asymptotic behavior of a probability density function for the sum of any two lognormally distributed random variables that are nontrivially correlated. We show that both the left and right tails can be approximated by some simple functions. Furthermore, the same techniques are applied to determine the tail probability density function for a ratio statistic, and for a sum with mo...

The paper shows an implementation model to support the execution of the Basic Andorra Model on distributed memory systems. A model for exploiting dependent AND parallelism in Prolog programs on distributed systems is also proposed, as well as the way in which it has to be combined with an OR parallel model. A mechanism for dealing with unbound variables in a distributed environment is proposed....

The expectations E[X(1)], E[Z(1)], and E[Y(1)] of the minimum of n independent geometric, modified geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E[X(1)]/E[Y(1)] equals the expected number of ties at the minimum for the geometric random variables. We then introduce the “shifted geometric distribut...

Frequently the need arises for the computer generation of variates that are exact/y distributed as 2 = max(X,, . , X.) where X,, . . . , X, form a sequence of independent identically distributed random variables. For large n the individual generation of the Xi’s is unfeasible, and the inversion-of-a-beta-variate is potentially inaccurate. In this paper, we discuss and compare the corrected inve...