Direct and inverse images for fractional stochastic tangent sets and applications

TL;DR

This paper investigates how fractional stochastic tangent sets behave under direct and inverse images, providing deterministic conditions for solutions of fractional Brownian motion-driven SDEs to stay within certain sets, along with a comparison theorem.

Contribution

It establishes deterministic necessary and sufficient conditions for solutions of fractional Brownian motion-driven SDEs to remain in specific sets, advancing the understanding of fractional stochastic tangent sets.

Findings

Derived deterministic conditions for solution containment in sets

Established a comparison theorem for fractional SDEs

Analyzed properties of fractional stochastic tangent sets

Abstract

In this paper, we study direct and inverse images for fractional stochastic tangent sets and we establish the deterministic necessary and sufficient conditions that guarantee that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets $K$. A comparison theorem is derived.