We propose to give stochastic bounds (both upper and lower bounds) based on convex order.
We show that, given stochastic independence, certain species of serial self-terminating models actually mandate the SCE.
In the output-feedback case the optimal H2 controller has the same order as the given stochastic system.
In particular this implies, under suitable assumptions, the existence of conditional densities for certain functionals of a given stochastic process.
A simulation example demonstrates how a stochastic T S fuzzy system can be constructed to realize the given stochastic process, approximately.
Recently, it was suggested that logistic regression could be used to relate the stochastic threshold to a defined probability of drop-out in order to properly evaluate the risks associated with a given stochastic threshold.
This method relies on a so-called convex lifting which is a nonnegative, convex, piecewise affine function, equal to 0 over a given stochastic positively invariant set and strictly positive outside this set.
A classical question in formal modelling with clear relevance to biological modelling is the model checking problem, i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process.
In this manner, it is possible to: (i) gain a much deeper insight into the dependence of relative permeability on the breadth and shape of the pore radius probability distribution as well as the network connectivity, and (ii) greatly simplify the approximate evaluation of the relative permeability of given stochastic networks under suitable conditions.
For a given stochastic basic, for, we set (1.7). in the case, we set.
