Theory of Probability &Its Applications, Volume 66, Issue 1, Page 15-43, January 2021.
A probabilistic approach to construction of the solution to the Cauchy problem for systems of nonlinear parabolic equations is developed. The systems under consideration can be subdivided into two classes: the systems of the first class can be interpreted, after a simple transformation, as systems of nonlinear backward Kolmogorov equations, and the systems of the second class as systems of nonlinear forward Kolmogorov equations. By choosing an appropriate interpretation, one can construct a stochastic model in terms of a stochastic equation with coefficients depending on the solution of the Cauchy problem under consideration and the closing relation corresponding to the probabilistic representation of this solution.

中文翻译：

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非线性后向和前向 Kolmogorov 方程组：广义解

Theory of Probability & Its Applications，第 66 卷，第 1 期，第 15-43 页，2021 年 1 月。开发了
一种概率方法来构造非线性抛物线方程系统的柯西问题的解。所考虑的系统可以细分为两类：第一类系统经过简单变换后可以解释为非线性后向 Kolmogorov 方程组，第二类系统可以解释为非线性前向 Kolmogorov 方程组。通过选择适当的解释，可以根据随机方程构建随机模型，该模型的系数取决于所考虑的柯西问题的解以及与该解的概率表示相对应的密切关系。