  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.
