arXiv subjects

David Márquez-Carreras

Publications and source records attributed to David Márquez-Carreras.

5 recordsLinked to original sources

arXiv2023

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

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.

math.PR↗

arXiv2020

Existence and smoothness of the density of the solution to fractional stochastic integral Volterra equations

We consider stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 . We first derive supremum norm estimates for the solution and its Malliavin derivative. We then show existence and smoothness of the density under suitable nondegeneracy conditions. This extends the results in Hu-Nualart and Nualart-Saussereau where stochastic differential equations driven by fractional Brownian motion are considered. The proof uses a priori estimates for deterministic differential equations driven by a function in a suitable Sobolev space.

math.PR↗

arXiv2015

Stability for a class of semilinear fractional stochastic integral equations

In this paper we study some stability criteria for some semilinear integral equations with a function as initial condition and with additive noise, which is a Young integral that could be a functional of fractional Brownian motion. Namely, we consider stability in the mean, asymptotic stability, stability, global stability and Mittag-Leffler stability. To do so, we use comparison results for fractional equations and an equation (in terms of Mittag-Leffler functions) whose family of solutions includes those of the underlying equation.

math.PR↗

arXiv2012

Anticipating Linear Stochastic Differential Equations Driven by a Lévy Process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformation on Wiener space and developped by Buckdahn to the canonical Lévy space.

math.PR↗

arXiv2012

Delay equations with non-negativity constraints driven by a Hölder continuous function of order βin (1/3,1/2)

In this note we prove an existence and uniqueness result of solution for multidimensional delay differential equations with normal reflection and driven by a Hölder continuous function of order $β\in (\frac13,\frac12)$. We also obtain a bound for the supremum norm of this solution. As an application, we get these results for stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H $\in (\frac13,\frac12)$.

math.PR↗