The search algorithm presented allows the CDF of a dependent variable to be bounded with 100% confidence, and allows for a guaranteed evaluation of the error involved. These reliability bounds are often enough to make decisions, and require a minimal number of function calls. The procedure is not intrusive, i.e. it can be equally applied when the function is a complex computer model (black box)...

The main purpose of this work is to contribute the study set-valued random variables by providing a kind Wold decomposition theorem for interval-valued processes. As set not vector space, as established in 1938 Herman applicable them. So, notion pseudovector space introduced and used establish generalization that works covariance stationary time series Before this, autoregressive moving-average...

Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the o...

The present paper is devoted to the transition from crisp domains of probability to fuzzy domains of probability. First, we start with a simple transportation problem and present its solution. The solution has a probabilistic interpretation and it illustrates the transition from classical random variables to fuzzy random variables in the sense of Gudder and Bugajski. Second, we analyse the proc...

Let X1,X2, ... be independent and symmetric random variables such that Sn = X1+ ...+Xn converges to a finite valued random variable S a.s. and let S = sup1≤n<∞ Sn (which is finite a.s.). We construct upper and lower bounds for sy and s ∗ y, the upper 1 y th quantile of Sy and S , respectively. Our approximations rely on an explicitly computable quantity q y for which we prove that 1 2 q y/2 < s...