Strongly and weakly harmonizable stochastic processes of H-valued random variables

The Wigner Distribution of Gaussian Weakly Harmonizable Stochastic Processes

The paper treats theWigner distribution of scalar-valued stochastic processes defined on R. We show that if the process is Gaussian and weakly harmonizable then a stochastic Wigner distribution is well defined. The special case of stationary processes is studied, in which case the Wigner distribution is weakly stationary in the time variable and the variance is equal to the deterministic Wigner...

Random Variables and Stochastic Processes

Stochastic relations of random variables and processes

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes, it suffices that the generators of the processes preserve some, not necessarily reflexive or transitive, subrelation of the order relation. The m...

Probability, random variables and stochastic processes

Generating Random Variables and Stochastic Processes

Some History • Earliest methods were manual – throwing dice, dealing cards, drawing balls from an urn • Mechanized devices in early 1900’s • Later, methods based on electric circuits • Many other schemes based on phone books, π etc. • Advent of computing led to interest in numerical and arithmetic methods – such methods generate numbers sequentially and are easily programmed – the most commonly...