A Bound for Continuous Martingales in a Cone

In this paper, we prove that, under a "non concentrating" condition, the class Q( C, M, p) of continuous martingales is uniformly bounded in L a, for an a > 1. C is here a closed cone of IR[exp. k] with pointed convex hull, p is a point of C, M is a closed cone of (K x I )-matrices and Q(C, M, p) denotes the class of C-valued martingales Y = p+fo· AtdBt , where A is a M-valued progressively measurable process on a filtration {Gt},and B a I-dimensional {Gt}-Brownian Motion. The "non concentrating" condition mentioned above is: [whatever]A [belong] M, [whatever]y [belong] C: AA[exp. T] = yy [exp. T] => A = O.