Abstract
Let P and P' be the laws of two discrete-time stochastic processes defined on the sequence
space S, where S is a finite set of points. In this paper we derive a bound on the total variation
distance dTV(P,P') in terms of the cylindrical projections of P and P'. We apply the
result to Markov chains with finite state space and random walks on Z with not necessarily
independent increments, and we consider several examples. Our approach relies on the general
framework of stochastic analysis for discrete-time obtuse random walks and the proof
of our main result makes use of the predictable representation of multidimensional normal
martingales. Along the way, we obtain a sufficient condition for the absolute continuity of
P' with respect to P which is of interest in its own right.
Anno
2019
Autori IAC
Tipo pubblicazione
Altri Autori
Ian Flint; Nicolas Privault; Giovanni Luca Torrisi
Editore
Kluwer Academic Publishers
Rivista
Potential analysis