MÉTHODES DE CHANGEMENT DE TEMPS POUR LA CONVERGENCE
EN LOI DES MARTINGALES
Abstract: Let be a centred, square integrable martingale, indexed by
or whose predictible quadratic variation is denoted by
The main problem we investigate is the study of the joint convergence in law, when
of the processes
where
and
are two increasing functions. To solve this problem we use three technical
tools (each of them having its one interest):
- a limit theorem for composed processes;
- a limit theorem for random change of time;
- a method of enlarging the probability space on which is defined.
This approach looks to be efficient as far as the asymptotic behaviour of functionals of
recurrent Markov or semi-Markov processes is concerned. Several examples illustrate the
developed theory.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -