集值上鞅的收敛定理及 Riesz 分解

本文给出了集值鞅的进一步性质;建立了集值上鞅外穿不等式;证明了一个集值上鞅收敛定理;研究了集值上鞅的 Riesz 分解.     

g-上鞅的Riesz分解定理

本文给出了当终端时间趋于无穷时一类有限时间区间上的倒向随机微分方程的解的收敛性,并且证明了这类解平方收敛到特定的无穷时间区间上的倒向随机微分方程的解.本文主要研究了由倒向随机微分方程生成的非线性期望及其鞅的性质,证明了当生成元g是超线性时的g-上鞅Riesz分解定理.并且指出经典鞅论中的Riesz分解定理和下期望(又称最小期望)对应的上鞅Riesz分解定理是g-上鞅Riesz分解定理的两种特殊情况.     

M.Riesz定理的注记

设u(z)是单位圆内的实值调和函数 ,若 p_平均Mp(r ,u) =12π∫2π0｜u(reiθ) ｜pdθ1 p <∞ ,则称u(z) ∈hp( 1

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