On explosion time in stochastic differential equations driven by fractional Brownian motion

TL;DR

This paper investigates the explosion time of solutions to stochastic differential equations driven by fractional Brownian motion with Hurst parameter greater than 1/2, introducing new analytical and numerical methods.

Contribution

It extends existing results to non-constant diffusion coefficients using Lamperti transformation and proposes an adaptive Euler-type scheme for approximation.

Findings

Extended analysis to non-constant diffusion coefficients

Developed an adaptive Euler-type numerical scheme

Provided insights into explosion times for fractional Brownian motion driven SDEs

Abstract

In this article, we study the explosion time of the solution to autonomous stochastic differential equations driven by the fractional Brownian motion with Hurst parameter $H>1/2$. With the help of the Lamperti transformation, we are able to tackle the case of non-constant diffusion coefficients not covered in the literature. In addition, we provide an adaptive Euler-type numerical scheme for approximating the explosion time.