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：针对带有乘性噪声的随机非线性抛物方程，我们提出了一种两点通量近似有限体积格式。时间离散采用隐式格式，但随机噪声项除外，以符合伊藤随机积分的要求。我们证明了该格式解的存在唯一性，并且由近似解的唯一性可得到随机积分所需的适当可测性。