两指标B值强鞅的收敛性与Banach空间的几何性质

Convergence of Two-parameter Banach Space Valued Strong Martingales and Geometrical Properties of Banach Space

证明了L1有界的两指标B值强鞅a.s.收敛的充分必要条件是Banach空间具有Radon-Nikodym性质,并进一步利用两指标B值强鞅的收敛性刻划了Banach空间的几何性质.

Any L1 bounding two-parameter Banach space valued strongmartingale converges almost surely to an integrable Banach Space valued random variable if and only if Banach space has the Radon-Nikodym property. Furthermore, the geometrical properties of Banach space are characterized by the convergence properties of two-parameter Banach space valued strong martingale.