对于反射的维纳,奥恩斯坦-乌伦贝克和费勒扩散过程的精确解决方案和非对称行为
Virginia Giorno1, Amelia G Nobile1
1Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo Ⅱ n. 132, 84084 Fisciano (SA), Italy.
Mathematical biosciences and engineering : MBE
|September 7, 2023
概括
本研究分析了零流量条件下的扩散过程,重点关注过渡概率和首次通道时间. 结果提供了对受限制的维纳,奥恩斯坦-乌伦贝克和费勒过程的见解,其中包括排队系统应用程序.
科学领域:
- 随机过程 随机过程
- 数学物理 数学物理
- 可能性理论概率理论.
背景情况:
- 扩散过程是模拟随机现象的基础.
- 零流量条件对于分析边界行为至关重要.
- 了解过渡概率和第一次通道时间是系统动态的关键.
研究的目的:
- 在零流量条件下分析过渡概率密度函数 (TPDF).
- 为了研究维纳,奥恩斯坦-乌伦贝克和费勒过程中这些TPDF的非对称行为.
- 研究第一通道时间时刻及其非对称行为,特别是在时间均的情况下.
主要方法:
- 对维纳,奥恩斯坦-乌伦贝克和费勒工艺的TPDF进行分析.
- 调查时间不均的比例和时间均的情况.
- 详细研究第一通道时间时刻及其非对称性质.
- 对于受限扩散过程中TPDF之间的关系的导出.
主要成果:
- 在零流量条件下TPDF及其非对称行为的表征.
- 对时间均扩散过程的第一通道时间时刻的非对称分析.
- 对于受限制的维纳,奥恩斯坦-乌伦贝克和费勒工艺的TPDF之间建立了关系.
- 对排队系统的发现的证明适用性.
结论:
- 该研究提供了在零流量条件下扩散过程的全面分析.
- 这些发现增强了对随机过程及其边界行为的理解.
- 结果对建模和分析队列系统和其他应用概率问题有直接影响.
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