一维非常返扩散过程的代数式退化

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 270-285.

一维非常返扩散过程的代数式退化

甘蕾蕾, 郝一菲, 王颖喆^*()

北京师范大学数学科学学院, 数学与复杂系统教育部重点实验室北京 100875

收稿日期:2025-01-21 修回日期:2025-06-27 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 王颖喆 E-mail:wangyz@bnu.edu.cn
基金资助:
国家重点研发计划(2020YFA0712900)

Algebraic Degeneration of One-Dimension Non-Recurrent Diffusion Processes

Leilei Gan, Yifei Hao, Yingzhe Wang^*()

School of Mathematical Sciences, Beijing Normal University, Key Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing 100875

Received:2025-01-21 Revised:2025-06-27 Online:2026-02-26 Published:2026-01-19
Contact: Yingzhe Wang E-mail:wangyz@bnu.edu.cn
Supported by:
Fund for National Key R&D Program of China(2020YFA0712900)

摘要/Abstract

摘要：

主要研究半直线上的非常返扩散过程在 $L^2$ 意义下代数式退化的情况, 得到两种边界条件下过程代数式退化的充分条件和必要条件, 并将相关结论推广到实直线上. 最后, 将所得结论应用在两个具体例子上, 得到了精确的结果.

关键词: 一维扩散过程, 非常返, 代数式退化

Abstract:

Algebraic degeneration in $L^2$ sense is studied for non-recurrent diffusion process on a semi-line. The sufficient and necessary conditions are presented under two boundary conditions. The similar conclusions are also proved on the real line. The conclusions are applied to two examples, yielding precise results.

Key words: one-dimension diffusion process, non-recurrent, algebraic degeneration

中图分类号:

O211.62

甘蕾蕾, 郝一菲, 王颖喆. 一维非常返扩散过程的代数式退化[J]. 数学物理学报, 2026, 46(1): 270-285.

Leilei Gan, Yifei Hao, Yingzhe Wang. Algebraic Degeneration of One-Dimension Non-Recurrent Diffusion Processes[J]. Acta mathematica scientia,Series A, 2026, 46(1): 270-285.

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