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Vol. 31 No. 1 (2026)

Probability and Statistics

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

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

Published 2025-11-10

  • Òscar Burés
    • ,
  • Carles Rovira

Òscar Burés
Universitat de Barcelona

Carles Rovira
Universitat de Barcelona

Abstract

In this paper, we prove that the density of a Stochastic Delay Differential equation driven by a fBm is strictly positive combining Nourdin-Viens’ and Kohatsu-Higa’s method.

Keywords

Stochastic delay equation, Malliavin calculus, fractional Brownian motion, Estimates of the density

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Supplementary File(s)

mc_5378_TEX mc_5378_bbl