L(p)空间倒向随机微分方程g-期望的性质

In this paper, we show that the classical g-expectation can be extended to L^{p} space when 1<p<2,and its extension is unique about the generator, and give the representation of the g-expectation in L^{p} space. We define the related conditional g-expectation via the g-expectation, proof its existence and niqueness, and also give its representation. We use Represention Theorem, Uniqueness Theorem for g-expectation and some properties of L^{p} solutions of Backwards Stochastic Differential Equations to study the g-expectation (resp. conditional g-expectation), get the Uniqueness Theorem, Translation Invariance Theorem and Subadditivity Theorem for the g-expectation.