论文标题
几乎确定核空间双重过程中随机过程的均匀收敛性
Almost Sure Uniform Convergence of Stochastic Processes in the Dual of a Nuclear Space
论文作者
论文摘要
令$φ$为核空间，让$φ'$表示其强双重。在本文中，我们为有限的时间间隔介绍了足够的条件，以$φ'$ - 有价值的过程具有连续的（分别是Càdlàg）路径。主要结果首先是在圆柱过程的一般环境中提出的，但后来专门针对其他感兴趣的情况。特别是，我们确定了将收敛发生在$φ'$中的希尔伯特空间中的条件。此外，在超生物学核空间的双重背景下（例如平滑函数和分布的空间），我们还将应用于一系列独立的Càdlàg工艺的收敛，以及解决方案对线性进化方程的收敛，这是由Lévy噪声驱动的。
Let $Φ$ be a nuclear space and let $Φ'$ denote its strong dual. In this paper we introduce sufficient conditions for the almost surely uniform convergence on bounded intervals of time for a sequence of $Φ'$-valued processes having continuous (respectively càdlàg) paths. The main result is formulated first in the general setting of cylindrical processes but later specialized to other situations of interest. In particular, we establish conditions for the convergence to occur in a Hilbert space continuously embedded in $Φ'$. Furthermore, in the context of the dual of an ultrabornological nuclear space (like spaces of smooth functions and distributions) we also include applications to the convergence of a series of independent càdlàg process and to the convergence of solutions to linear evolution equations driven by Lévy noise.
