As we explained in the "Introduction," there are, however, important cases where the insurer's information does not take the form of a single probability measure
over a space of relevant scenarios.
In this sense, it is a cumulative probability measure
for the question at hand.
Then, on (H(D), B(H(D))), there exists a probability measure
[P.sub.[alpha],a] such that [P.sub.T,[alpha],a] converges weakly to [P.sub.[alpha],a] as T [right arrow] to.
Application to Knightian/Misesian framework: When Knight (or Mises, for that matter) identifies risk with (a frequency interpretation of) probability, he does not pass this test because then it is not differentiated between the notion (i.e., risk and hence probability) and its operationalization (i.e., the probability measure
"The OIS, if you use it as a probability measure
, is at about a 79 percent chance of a rate hike in July.
Then, there exist a unique compact set K and a unique probability measure
[mu] on K such that K = [[union].sup.N.sub.i=1] [f.sub.i](K) and
Let [mu] be a probability measure
on R such that a family of [mathematical expression not reproducible]-orthonormal polynomials [mathematical expression not reproducible] can be defined.1 The non-decreasing function
Now, we consider that [mu] is a probability measure
on the compact set X, which is unnecessarily absolutely continuous measure with respect to Lebesgue measure [lambda].
As before, we denote by [mu], a probability measure
on [R.sup.l], the common law of the i.i.d.
Given the dynamics of the underlying asset price and the counterparty's asset value under the probability measure
Q, it is possible to obtain the joint moment generating function of ln S(T) and ln V(T).
These probabilities are defined starting from previous works on linguistic probability [29-32] defining similar probability measure
for fuzzy probabilities.
In quantum information theory, when one needs to understand properties of typical density matrices, it is necessary to endow the convex body of quantum states with a natural, physically motivated probability measure
, in order to compute statistics of the relevant quantities.