Abstract:We prove anomalous-diffusion scaling for a one-dimensional stochastic kinetic dynamics, in which the stochastic drift is driven by an exogenous self-similar noise, and also includes endogenous volatility which is permitted to have arbitrary dependence with the exogenous noise. We identify the superdiffusive scaling exponent for the model, and prove strong and weak convergence results on the corresponding scale. Our framework admits self-similar noise that is either a Bessel process, or, more generally, a self-similar continuous-state branching process with immigration, as well as more general processes satisfying certain asymptotic conditions.
From: Andrew R. Wade [view email]
[v1]
Mon, 22 Jan 2024 11:33:25 UTC (866 KB)
[v2]
Wed, 5 Feb 2025 06:54:55 UTC (868 KB)
[v3]
Thu, 10 Sep 2026 12:23:15 UTC (873 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。