Abstract: In this paper, the authors explore the solution (y,z) of BSDEs via the theory of Malliavin derivative. Some methods of comparing part z have been given. And the authors point out that the comonotonic theorems for part z given by Zengjing Chen et al (see [3]) aren't correct when the generators of BSDEs are stochastic. Thus some special conditions, under which the comonotonic theorems for part z are correct even the generators of BSDEs are stochastic, are studied. Then, applying the comonotonic theorems, the authors study the additivity of a class of conditional g-expectations and Choquet integral represention theorems.

Key words: BSDE, Malliavin derivative, g -expectation, Choquet integral.