Riassunto analitico
In the study of Markov processes a key tool is provided by duality theory, that allows to study the original process via a simpler one, called the dual process.
In this work we consider a diffusion process in the three-dimensional space for which both total energy (i.e. sum of the square of the variables) and momentum (i.e. sum of the variables) are conserved.
We find a dual process by combining: i) a change of representation of the su(1,1) Lie algebra; ii) a change of coordinates given by a rotation.
As a consequence we characterize the invariant measure of the original process.
Furthermore, we develop a general theory of duality under change of coordinates.
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