We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The $L^2$ estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes.
翻译:本文针对低正则速度场下的随机输运方程,提出了差分格式。我们在比确定性输运方程所需条件更宽松的条件下,建立了差分近似的$L^2$稳定性与收敛性。分析中关键的$L^2$估计通过离散对偶论证以及对一类后向抛物型差分格式的全面考察获得。