Proposition 4 Let ⪯ ˜ be an integral stochastic order on P and ⪯ be the partial order on X determined by ⪯ ˜.
Theorem 1 Let ⪯ ˜ be an integral stochastic order on P and ⪯ be the partial order on X determined by ⪯ ˜.
Next, we prove that P ⪯ g Q implies P ⪯ ˜ Q. Proposition 3 Let ⪯ ˜ be an integral stochastic order on P. Let ⪯ be the partial order on X determined by ⪯ ˜.
Note that, in general, if ℛ is a generator of a stochastic order and g and f are ⪯-comonotonic functions for all f ∈ R, g is not necessarily an element of ℛ.
Proposition 2 Let ⪯ ˜ be an integral stochastic order on P and R 1 and R 2 be generators of the order.
If, is updated as, where is the learning parameter controlling the size of the change to W. Because SGD is a stochastic method, the order of the training instances is randomized after each iteration; the final and performance therefore vary slightly.
A stochastic order is defined as a partial order relation on a set of probabilities associated with a certain measurable space, although in some contexts the antisymmetric condition is not considered.
The test chosen is based on a stochastic ordering.
RESIC is a stochastic process model to identify the order of mutations (Attolini et al., 2010), which successfully confirmed the results in colorectal cancer, suggesting that cross-sectional data is informative for the prediction of mutation order.
Let (X t)) be a second order stochastic process, mean square continuous on (I=[t_{0},T]), then there exists (etain I) such that int_{t_{0}}^{t}X s),ds=X eta) (t-t_{0}), quad t_{0}< t<T.
