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Martingale representation in uniformly convex spaces

Authors: D. Landers and L. Rogge
Journal: Proc. Amer. Math. Soc. 75 (1979), 108-110
MSC: Primary 60G48
MathSciNet review: 530761
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Abstract: In this paper we define the concept of a martingale in a uniformly convex Banach space and show that each bounded martingale is convergent and can be represented as a sequence of nearest point projections onto closed convex sets of one element of the Banach space. This result contains classical representation theorems for usual martingales and yields applications in the theory of nearest point projections in $ {L_p}$-spaces.

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Keywords: Martingale, uniformly convex Banach space, conditional expectation
Article copyright: © Copyright 1979 American Mathematical Society

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