Generation of random dynamical systems from fractional stochastic delay differential equations

TL;DR

This paper proves that certain fractional stochastic delay differential equations generate continuous random dynamical systems on a separable H"older space, expanding understanding of their mathematical structure.

Contribution

It establishes the existence of continuous random dynamical systems for fractional stochastic delay differential equations under natural regularity conditions.

Findings

Generates a continuous random dynamical system on a separable H"older space.

Provides a mathematical foundation for analyzing fractional stochastic delay differential equations.

Extends the theory of random dynamical systems to fractional stochastic delay equations.

Abstract

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a H\"older space which is separable.