Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces

TL;DR

This paper investigates the weak convergence of error processes in discretized stochastic integrals, linking the limit's integrability to the fractional smoothness in the Malliavin calculus framework.

Contribution

It establishes a connection between the weak convergence of discretization errors and the fractional smoothness of stochastic integrals in Besov spaces.

Findings

Weak convergence of error processes is characterized.

The $L_p$-integrability of the limit relates to Malliavin fractional smoothness.

Results apply to Riemann discretizations of stochastic integrals.

Abstract

We consider weak convergence of the rescaled error processes arising from Riemann discretizations of certain stochastic integrals and relate the $L_p$-integrability of the weak limit to the fractional smoothness in the Malliavin sense of the stochastic integral.