This paper presents a link between unbalanced non-linear urn model (a two-colored urn model) and stochastic approximation theory. Findings of our study reveal a successful establishment of limit laws for the urn composition, obtained under a drawing rule reinforced by an \(\mathbb {R}_{+}\)-valued concave function and a non-balanced replacement matrix.

中文翻译：

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随机逼近的非线性不平衡Ur模型

本文提出了非平衡非线性模型（两色模型）与随机逼近理论之间的联系。我们的研究结果表明，成功建立了骨灰盒组成的极限定律，该极限定律是在由\（\ mathbb {R} _ {+} \）值凹函数和非平衡置换矩阵所增强的绘图规则下获得的。