Giorno Virginia, Nobile Amelia G
Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo Ⅱ n. 132, 84084 Fisciano (SA), Italy.
Math Biosci Eng. 2023 Jun 14;20(8):13602-13637. doi: 10.3934/mbe.2023607.
We analyze the transition probability density functions in the presence of a zero-flux condition in the zero-state and their asymptotic behaviors for the Wiener, Ornstein Uhlenbeck and Feller diffusion processes. Particular attention is paid to the time-inhomogeneous proportional cases and to the time-homogeneous cases. A detailed study of the moments of first-passage time and of their asymptotic behaviors is carried out for the time-homogeneous cases. Some relationships between the transition probability density functions for the restricted Wiener, Ornstein-Uhlenbeck and Feller processes are proved. Specific applications of the results to queueing systems are provided.
我们分析了在零状态下存在零通量条件时维纳过程、奥恩斯坦 - 乌伦贝克过程和费勒扩散过程的转移概率密度函数及其渐近行为。特别关注了时间非齐次比例情形和时间齐次情形。对时间齐次情形下首次通过时间的矩及其渐近行为进行了详细研究。证明了受限维纳过程、奥恩斯坦 - 乌伦贝克过程和费勒过程的转移概率密度函数之间的一些关系。给出了这些结果在排队系统中的具体应用。
