6 papers
A note on compact Markov operators
Fabio Zucca
The analytic properties of the Markov operator associated to a random walk are common tools in the study of the behaviour and some probabilistic features related to the walk. In th…
Strong and weak mean value properties on trees
Fabio Zucca
We consider the mean value properties for finite variation measures with respect to a Markov operator in a discrete environnement. We prove equivalent conditions for the weak mean…
Classification on the average of random walks
Daniela Bertacchi, Fabio Zucca
We introduce a new method for studying large scale properties of random walks. The new concepts of transience and recurrence on the average are compared with the ones introduced by…
On some properties of transitions operators
Fabio Zucca
We study a general transition operator, generated by a random walk on a graph ; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transi…
Uniform asymptotic estimates of transition probabilities on combs
Daniela Bertacchi, Fabio Zucca
We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular we obtain space-time uniform asymptotical estimates…
On a class of stochastic differential equations used in quantum optics
Alberto Barchielli, Fabio Zucca
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such eq…