Third, we control for additional standard market return predictors, including the consumption-wealth ratio (CAY), dividend yield (DY), earnings-price ratio (EP), default premium (DEF), term premium (TERM), and stochastically
detrended risk-free rate (RREL).
The idea is to determine the KH breakup time dynamically and stochastically
using a probability distribution function (PDF) with shape parameters depending on local flow conditions.
The exact probability-based analysis using multidimensional integrals of the systems having stochastically
dependent components is also very difficult.
These values are consistent with an upper bound estimate of a micro-crack size of less than 200 [micro]m from the diameter of the protrusions seen forming stochastically
along the crack tip in the X-ray images.
For positive system (1) and a given [gamma] > 0, system (1) is stochastically
stable and satisfies [mathematical expression not reproducible] if and only if there exist vectors [p.
Renewable sources are stochastically
variable, thereby negatively affecting power system operator situational awareness--the ability to interpret current operation status and potential problems.
alpha]] : average profit values obtained under one strategy are stochastically
smaller than the ones obtained under the other strategy
Furthermore, with the exception of one larger contribution, the distribution of contributions in the competitive treatment first order stochastically
dominates that of the cooperative treatment.
xy] it is possible to test whether the symbols observed are stochastically
linearly independent or dependent.
Monotonicity: If one portfolio is first-order stochastically
dominant in that it offers higher returns in every state, then the risk associated with that portfolio cannot be higher than that of any other.
This remark equally concerns the debt servicing costs, when the interest on borrowed funds is often linked with stochastically
changing global financial parameters and also when the violation of debt conditions traditionally changes the parameters of costs.
Nature responds to this choice by selecting an outcome stochastically
according to the probability rule given by quantum theory.