  For a series of Markov processes we prove stochastic duality relations with
duality functions given by orthogonal polynomials. This means that expectations
with respect to the original process (which evolves the variable of the
orthogonal polynomial) can be studied via expectations with respect to the dual
process (which evolves the index of the polynomial). The set of processes
include interacting particle systems, such as the exclusion process, the
inclusion process and independent random walkers, as well as interacting
diffusions and redistribution models of Kipnis-Marchioro-Presutti type. Duality
functions are given in terms of classical orthogonal polynomials, both of
discrete and continuous variable, and the measure in the orthogonality relation
coincides with the process stationary measure.
