Martingales à valeurs fermées bornées d’un espace métrique. (Martingales with values in closed bounded subsets of a metric space).(French)Zbl 0652.60015

We give [developing an idea of S. Doss,onal empirical processes for $$\Phi$$-mixing and a-mixing stochastic vectors to appropriate Gaussian processes under weaker conditions than K. J. Yoshihara [Z. Wahrscheinlichkeitstheor. Verw. Geb. 33, 133-137 (1975; Zbl 0304.60019)], i.e. either $\sum \Phi^{1/2}(2^ n)<\infty,\quad or\quad a(n)=O(n^{-r}),$ where $$r>2$$, if $$p=1$$; $$r>p+1$$, if $$p\geq 2$$ and even; $$r>p^ 2/(p-1)$$, if $$p\geq 3$$ and odd.

MSC:

 60B99 Probability theory on algebraic and topological structures 60G44 Martingales with continuous parameter

Zbl 0304.60019