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

2023/02/07 by Mireia Besalú, Besalú, Mireia, David Márquez‐Carreras +3
Economics, Econometrics and Finance · Mathematics · Computer Science · #Stochastic processes and financial applications #Nonlinear Differential Equations Analysis #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2302.03345

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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