本文证明了d维半鞅X = M + A的凸函数f的局部鞅部分可以表示为It^o随机积分\int H（X）dM，其中H（x）是f在x处的次梯度的某种特殊可测选择，M是X的鞅部分.这个结果首先由Bouleau在[2]中证明。在这里，我们提出了一个新的处理问题。我们首先证明了X' = X + eB，e > 0的结果，其中B是标准布朗运动，然后利用[1]和[4]中的结果，当e趋于0时，我们得到极限.
英文摘要：
In this note we prove that the local martingale part of a convex function f of a d-dimensional semimartingale X = M + A can be written in terms of an It^o stochastic integral \int H(X)dM, where H(x) is some particular measurable choice of subgradient of f at x, and M is the martingale part of X. This result was first proved by Bouleau in [2]. Here we present a new treatment of the problem. We first prove the result for X' = X + eB, e > 0, where B is a standard Brownian motion, and then pass to the limit as e tends to 0, using results in [1] and [4].
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