Intuition based on the usual interpretation of the covariance of two random variables suggests that the inequality cov[f(X),g(X)]≥0 should hold for any random variable X and any two increasing functions f and g. The inequality holds indeed, but a proof is hard to find in the literature. In...

For certain types of stochastic processes {Xn n [set membership, variant] }, which are integrable and adapted to a nondecreasing sequence of [sigma]-algebras n on a probability space ([Omega], , P), several authors have studied the following problems: IfSdenotes the class of all stopping times...

Through the decomposition theorem of Lebesgue and Darst it is possible to define a generalized Radon-Nikodym derivative of a bounded additive set function with respect to a bounded countably additive set function. For a bounded amart the derivatives of the components are shown to converge almost...