In this paper, we consider two versions of functional equations for the stochastic exponential. One equation for a function of a semimartingale and its square characteristic and the second for non-anticipative functionals. A martingale characterization of the general solutions of these equations is given.

中文翻译：

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随机指数的函数方程

在本文中，我们考虑随机指数函数方程的两个版本。第一个方程用于半鞅函数及其平方特征，第二个方程用于非预期泛函。给出了这些方程通解的鞅表征。