由 Lévy 过程驱动的有限记忆自排斥扩散的遍历性与大数定律
Ergodicity and the Strong Law of Large Numbers for Finite-Memory Self-Repelling Di?usions Driven by Lévy Processes
摘要: 本文研究由一维 Lévy 过程驱动的有限记忆自排斥扩散过程 XT (t)。将该过程的路径增量构造为 Skorokhod 空间 D[0, T ] 上的马尔可夫链并证明了该链的 Harris 正常返性以及其不变测度的有限性, 由此得出该过程的强大数定律。
Abstract: This paper investigates a finite-memory self-repelling diffusion process XT (t) driven by a one-dimensional Lévy process. By formulating the path increments of the process as a Markov chain on the Skorokhod space D[0, T ], we establish the Harris recurrence of the chain and the finiteness of its invariant measure. Consequently, the strong law of large numbers for this process is derived.
文章引用：杨毅, 田琳琳, 闫理坦. 由 Lévy 过程驱动的有限记忆自排斥扩散的遍历性与大数定律[J]. 应用数学进展, 2026, 15(5): 156-165. https://doi.org/10.12677/AAM.2026.155216

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