Superdiffusive limits for Bessel-driven stochastic kinetics

TL;DR

This paper establishes superdiffusive scaling limits for a one-dimensional stochastic kinetic model driven by Bessel noise, extending to more general noise processes and proving weak convergence results.

Contribution

It introduces a novel superdiffusive scaling limit for Bessel-driven stochastic kinetics and generalizes the results to broader classes of noise processes.

Findings

Identifies the superdiffusive scaling exponent for the model

Proves weak convergence on the scaled process

Extends results to general noise processes satisfying asymptotic conditions

Abstract

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.