Abstract Dynamical systems driven by two or multi-timescales arise in systems science, natural and social sciences quite naturally. Work done by Vivek S. Borkar (1997) on stochastic approximation driven by two timescales and later by others pave the pathway for wide applications of such systems. In this article we provide weak convergence of such systems for the linear case.

中文翻译：

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动态系统在两个时间尺度上的弱收敛

摘要 由两个或多个时间尺度驱动的动力系统很自然地出现在系统科学、自然科学和社会科学中。Vivek S. Borkar (1997) 关于由两个时间尺度驱动的随机近似以及后来其他人所做的工作为此类系统的广泛应用铺平了道路。在本文中，我们为线性情况提供了此类系统的弱收敛。