# Strong convergence rates for Markovian representations of fractional processes

## TL;DR

This paper investigates the numerical discretization of Markovian representations of fractional processes, demonstrating high-order strong convergence rates and analyzing their implications for Monte Carlo methods in fractional volatility modeling.

## Contribution

It establishes that discretizations of these representations can achieve arbitrarily high polynomial order convergence, clarifying their effectiveness and limitations in Monte Carlo simulations.

## Key findings

- Discretizations have strong convergence rates of arbitrarily high polynomial order.
- The representation's potential for Monte Carlo schemes is confirmed, but with noted limitations.
- Insights into fractional volatility models like the rough Bergomi model are provided.

## Abstract

Many fractional processes can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily high polynomial order. This explains the potential, but also some limitations of such representations as the basis of Monte Carlo schemes for fractional volatility models such as the rough Bergomi model.