Stochastic affine evolution equations with multiplicative fractional noise
Bohdan Maslowski, Jana \v{S}nup\'arkov\'a
TL;DR
This paper investigates stochastic affine evolution equations driven by fractional Brownian motion, establishing existence, uniqueness, and analyzing long-term behavior of solutions within the Skorokhod integration framework.
Contribution
It introduces a novel analysis of affine evolution equations with bilinear fractional noise, proving existence and uniqueness of solutions and exploring their asymptotic properties.
Findings
Existence and uniqueness of weak solutions are established.
Long-term dynamics of solutions are characterized.
The study extends stochastic evolution theory to fractional noise contexts.
Abstract
A stochastic affine evolution equation with bilinear noise term is studied where the driving process is a real-valued fractional Brownian motion. Stochastic integration is understood in the Skorokhod sense. Existence and uniqueness of weak solution is proved and some results on the large time dynamics are obtained
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