We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible with stochastic integration in the sense of It\^{o}. We show existence and uniqueness of solutions to the scheme and the appropriate measurability for stochastic integration follows from the uniqueness of approximate solutions.

翻译：我们提出了一种用于随机非线性抛物方程的二点通量逼近有限体积格式。时间离散化是隐式的，除了随机噪声项外，为了与Itô的随机积分兼容。我们证明了方案的解的存在性和唯一性，并且适当的测量性质对于随机积分来说也应从近似解的唯一性得到。