Skip to the main content

Mathematical Communications, Vol. 31 No. 1, 2026.

Original scientific paper

https://doi.org/10.64785/mc.31.1.9

Gaussian lower bound and positivity of the density of stochastic delay differential equations driven by a fractional Brownian motion

Òscar Burés orcid id orcid.org/0009-0003-1741-1308 ; Departament de Matemàtica Econòmica, Financera i Actuarial, Facultat d’Economia i Empresa, Universitat de Barcelona, Barcelona, Spain *
Carles Rovira ; Departament de Matemàtiques i Informàtica, Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain

* Corresponding author.

Full text: english pdf 458 Kb

page 115-135

downloads: 72

cite

Abstract

In this paper, we prove that the density of a stochastic delay differential equation driven by a fBm with Hurst
parameter 𝐻 > 1/2 is strictly positive combining Nourdin-Viens’ and Kohatsu-Higa’s method.

Keywords

Stochastic delay equation; Malliavin calculus; fractional Brownian motion; estimates of the density

Hrčak ID:

345982

URI

https://hrcak.srce.hr/345982

Publication date:

2.4.2026.

Visits: 197 *