We provide a very brief introduction to typical paths and the corresponding Itô type integration. Relying on this robust Itô integration, we prove an existence and uniqueness result for one-dimensional differential equations driven by typical paths with non-Lipschitz continuous coefficients in the spirit of Yamada–Watanabe as well as an approximation result in the spirit of Doss–Sussmann.

中文翻译：

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一维博弈论微分方程

我们对典型路径和相应的Itô类型集成进行了非常简短的介绍。依靠这种强大的Itô积分，我们证明了由Yamada–Watanabe精神，由具有非Lipschitz连续系数的典型路径驱动的一维微分方程的存在性和唯一性，以及Doss–Sussmann精神的近似结果。