A celebrated result by A. Ionescu Tulcea provides a construction of a probability measure on a product space given a sequence of regular conditional probabilities. We study how the perturbations of the latter in the total variation metric affect the resulting product probability measure.

We apply our general method of duality, introduced in Giardinà et al. (2007), to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions...