Superdiffusive limits for Bessel-driven stochastic kinetics

Autor:	Brešar, Miha, da Costa, Conrado, Mijatović, Aleksandar, Wade, Andrew
Rok vydání:	2024
Předmět:	Mathematics - Probability 60J60 (Primary) 60K50 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We prove anomalous-diffusion scaling for a one-dimensional stochastic kinetic dynamics, in which the stochastic drift is driven by an exogenous Bessel 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 a weak convergence result on the corresponding scale. We show how our result extends to admit, as exogenous noise processes, not only Bessel processes but more general processes satisfying certain asymptotic conditions. Comment: 15 pages, 1 figure, for a short YouTube video describing the results, see https://youtu.be/O20plic5Ko8?si=-cg5XGdZlkO9WvYr
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.11863 Zobrazit plný text záznamu View this record from Arxiv