Viability for stochastic differential equations driven by fractional Brownian motion

TL;DR

This paper establishes viability conditions for multidimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter between 1/2 and 1, using a pathwise approach, and provides an alternative global existence result under state restrictions.

Contribution

It introduces a viability theorem for fractional SDEs with Hurst parameter in (1/2, 1) and offers a new global existence criterion for fractional differential equations.

Findings

Proves viability for multidimensional fractional SDEs with H in (1/2, 1)

Provides an alternative global existence result under state restrictions

Uses a pathwise approach for the analysis

Abstract

In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is also an alternative global existence result for the fractional differential equations with restrictions on the state.