Ten teams submitted predictions that were significantly better than random concerning at least two of the three applied performance measures.
Note that, by (29), the random variables concerned in (14) and (28) have finite moments of each order.
Another related source of risk is the information associated with the random time concerning resulting payments, the price impact, the loss given default or the recovery rate, etc. Measuring these random quantities is, in general, difficult since the relevant information on the underlying firm is often not accessible to investors on the market.
The notion of h-integrability for an array of random variables concerning an array of constants { a n k } is as follows.
In this paper, a new concept of weighted integrability is introduced for an array of random variables concerning an array of constants, which is weaker than other previous related notions of integrability.
Ordóñez Cabrera and Volodin [6] introduced the notion of h-integrability for an array of random variables concerning an array of constant weights, and proved that this concept is weaker than Cesàro uniform integrability, { a n i } -uniform integrability and Cesàro α-integrability.
Ordóñez Cabrera and Volodin [13] introduced the notion of h-integrability for an array of random variables concerning an array of constants { a n k } and showed that this concept is weaker than Cesàro uniform integrability, { a n k } -uniform integrability and Cesàro α-integrability.
When multiple random variables are concerned, we use the total correlation[14], which is one of several generalizations of the MI in probability theory and in particular in information theory, to express the amount of dependency existing among the variables.
In Section 2, we introduce basic concepts concerning random dynamical systems and random attractors for non-autonomous random dynamical systems.
When the distribution of stresses is concerned, a random foam shows a region of much higher stress concentration than regular lattices, owing to the random orientation of the struts in space.
