An Increment-Type Set-Indexed Markov Property

A Markov Property For Set-Indexed Processes

We consider a type of Markov property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A set-indexed generator is defined such that it completely characterizes the distribution of the process.

The Set-indexed Bandit Problem

An Alternative Markov Property for Chain Graphs

Graphical Markov models use graphs ei ther undirected directed or mixed to rep resent possible dependences among statis tical variables Applications of undirected graphs UDGs include models for spatial de pendence and image analysis while acyclic directed graphs ADGs which are espe cially convenient for statistical analysis arise in such elds as genetics and psychomet rics and as models for exp...

Random Fractals and Tree - Indexed Markov

We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the Moran-like deterministic or random recursive constructions considered by various authors. Among other applications, we consider various extensions of Mandelbrot's...

Type - indexed data