基于 Girsanov耦合的 Lévy驱动自排斥扩散的强大数定律
Strong Law of Large Numbersfor Lévy-Driven Self-RepellingDi?usions via Girsanov Coupling
摘要: 本文研究由一维 Lévy过程驱动的自排斥扩散的长时间渐近行为 ,利用 Girsanov定理进行随机耦合,严格证明了该无穷维非马尔可夫过程的强大数定律,确立了其严格正的渐近漂移速度。
Abstract: This paper investigates the long-time asymptotic behavior of self-repelling diffusion-s driven by a one-dimensional Lévy process. Utilizing a stochastic coupling based on Girsanov’s theorem, we rigorously prove the strong law of large numbers for this infinite-dimensional non-Markovian process and establish its strictly positive asymp-totic drift velocity.
文章引用：杨毅, 田琳琳, 闫理坦. 基于 Girsanov耦合的 Lévy驱动自排斥扩散的强大数定律[J]. 统计学与应用, 2026, 15(5): 158-167. https://doi.org/10.12677/SA.2026.155116

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