Existence of density for the solution of stochastic delay differential equations with reflection driven by a fractional Brownian motion

Mireia Besalú; David Márquez-Carreras; Carles Rovira

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arXiv · 2302.03345

Existence of density for the solution of stochastic delay differential equations with reflection driven by a fractional Brownian motion

Mireia Besalú·David Márquez-Carreras·Carles Rovira

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Abstract

In this note we prove the existence of a density for the law of the solution for 1-dimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H > 1/2$. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann-Stieltjes integral.

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Mireia Besalú, David Márquez-Carreras, Carles Rovira. 2023-02-07. Existence of density for the solution of stochastic delay differential equations with reflection driven by a fractional Brownian motion. https://arxiv.org/abs/2302.03345

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