AZÉMA MARTINGALES WITH DRIFT
Abstract: Pursuing the earlier work of Emery [1], Meyer [2], [3] and the author [4] it is shown
that Azéma martingales starting from a varying initial point on the line constitute an
Evans-Hudson flow in the framework of quantum stochastic calculus. A new transformation
property of Azéma martingales is established. It turns out, rather remarkably, that the Azéma
martingales and a class of their Weyl perturbations satisfy the same Itô’s formula but, in the
vacuum state, have very different asymptotic statistical properties as time increases to infinity.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -