A GENERAL CONTRACTION PRINCIPLE FOR VECTOR-VALUED
MARTINGALES
Abstract: We prove a contraction principle for vector-valued martingales of type
where
is a Banach space with elements
a martingale
difference sequence belonging to a certain class,
a sequence of
independent and symmetric random variables exponential in a certain sense, and
operators mapping each
into a non-negative random variable. Moreover, special
operators
are discussed and an application to Banach spaces of Rademacher type
is given.
1991 AMS Mathematics Subject Classification: 46B09, 60G44.
Key words and phrases: Vector-valued martingales, exponential random variables,
operators defined on martingales, contraction principle.