Linear time-varying stochastic differential equations with a.s. convergent continuous random system matrix processes are considered. It is shown that given the limit is known to be Hurwitz (i.e. asymptotically stable), the generated state solutions are a.s. bounded. This property is shown to hold by substantiating that, w.p.1, (i) no finite escape time exists and (ii) no divergence to infinity, as $t\to \mathrm{\infty }$, may occur. An application to stochastic adaptive control is provided.

中文翻译：

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由具有 Hurwitz 极限的收敛系统矩阵过程驱动的线性 SDE 的有界解

考虑了具有收敛连续随机系统矩阵过程的线性时变随机微分方程。结果表明，如果已知极限是 Hurwitz（即渐近稳定），则生成的状态解是有界的。通过证实 wp1，(i) 不存在有限的逃逸时间和 (ii) 不发散到无穷大，证明了这个性质是成立的，如$吨\to \mathrm{\infty }$， 可能导致。提供了对随机自适应控制的应用。