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2023•arXiv (Cornell University)Open access

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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What this paper is about

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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Available 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.

Key concepts: Fractional Brownian motion, Stochastic differential equation, Geometric Brownian motion, Mathematics, Reflected Brownian motion, Brownian motion, Reflection principle (Wiener process), Mathematical analysis

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