Superdiffusive limits for Bessel-driven stochastic kinetics

Superdiffusive limits for Bessel-driven stochastic kinetics

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 superdiffusi...

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Bibliographic Details
Main Authors: Brešar, Miha, da Costa, Conrado, Mijatović, Aleksandar, Wade, Andrew
Format: Journal Article
Language:English
Published: 22-01-2024
Subjects:
Mathematics - Probability
Online Access:Get full text
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Summary: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.
DOI:10.48550/arxiv.2401.11863