Remarks on invariant functions in Markov processes

Remarks on Non - Markov Processes

It is emphasized that non-Markovian processes, which occur for instance in the case of colored noise, cannot be considered merely as corrections to the class of Markov processes but require special treatment. Many familiar concepts, such as rst-passage times, no longer apply and need be reconsidered. Several methods of dealing with non-Markov processes are discussed. As an example a recent appl...

ON THE INFINITE ORDER MARKOV PROCESSES

The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.

Discrete Time Scale Invariant Markov Processes

In this paper we consider a discrete scale invariant Markov process {X(t), t ∈ R} with scale l > 1. We consider to have some fix number of observations in every scale, say T , and to get our samples at discrete points α, k ∈ W, where α is obtained by the equality l = α and W = {0, 1, . . .}. So we provide a discrete time scale invariant Markov (DT-SIM) process X(·) with parameter space {α, k ∈ ...

INVARIANT MEASURES FOR MARKOV PROCESSES(i)

Remarks on Classical Invariant Theory

A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.