A singular SDE driven by additive fractional Brownian motion with Hurst parameter H<1/2

TL;DR

This paper investigates a class of singular stochastic differential equations driven by fractional Brownian motion with Hurst parameter less than 1/2, focusing on solution construction and trajectory properties.

Contribution

It introduces a method to construct solutions as limits of approximating processes for SDEs driven by fractional Brownian motion with H<1/2.

Findings

Solutions can be constructed as limits of approximations.

Trajectory properties of solutions are characterized.

The approach extends understanding of SDEs with rough fractional noise.

Abstract

In this article we study a class of singular stochastic differential equations driven by fractional Brownian motion with Hurst parameter H<1/2. The solution is constructed as the limit of a family of approximating processes, and its trajectory properties are investigated.