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.

Riesz Decomposition Theorem of g-supermartingale

This paper gives the convergence of solutions via a class of backward stochastic differential equations(for short BSDEs) on finite time interval as the terminal time tends to infinite,and proves that the limit of these solutions square converges to the solution of a special BSDE on infinite time interval.This paper proves not only some properties of g-expectation generated by BSDEs and their martingales,but also the Riesz decomposition theorem of g-supermartingale when the generator of BSDE is superlinear.Prom this Riesz decomposition theorem we get the classical Riesz decomposition theorem of supermartingale and the Riesz decomposition theorem of supermartingale with respect to lower-expectation(also known as minimum expectation) immediately.