The fourth edition of this successful text provides an introduction to probability and random processes, with many practical applications. It is aimed at mathematics undergraduates and postgraduates, ...

Random fields and Gaussian processes constitute fundamental frameworks in modern probability theory and spatial statistics, providing robust tools for modelling complex dependencies over space and ...

A fundamental identity, due to Miller (1961a), (1962a, b) and Kemperman (1961), is generalized to semi-Markov processes. Thus the identity applies to processes defined on a Markov chain with discrete ...

Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

The entropy score of an observed outcome that has been given a probability forecast p is defined to be -log p. If p is derived from a probability model and there is a background model for which the ...

We start by embedding probability theory into a general theory of measure and integration. This will allow us to derive theorems that may not have been included in the Analysis III course but that are ...

Stochastic processes are at the center of probability theory, both from a theoretical and an applied viewpoint. Stochastic processes have applications in many disciplines such as physics, computer ...

Random processes take place all around us. It rains one day but not the next; stocks and bonds gain and lose value; traffic jams coalesce and disappear. Because they’re governed by numerous factors ...