arXiv subjects

Jorge A. Leon

Publications and source records attributed to Jorge A. Leon.

5 recordsLinked to original sources

arXiv2024

On explosion time in stochastic differential equations driven by fractional Brownian motion

In this article, we study the explosion time of the solution to autonomous stochastic differential equations driven by the fractional Brownian motion with Hurst parameter $H>1/2$. With the help of the Lamperti transformation, we are able to tackle the case of non-constant diffusion coefficients not covered in the literature. In addition, we provide an adaptive Euler-type numerical scheme for approximating the explosion time.

math.PR↗

arXiv2012

A strong uniform approximation of sub-fractional Brownian motion

Sub-fractional Brownian motion is a process analogous to fractional Brownian motion but without stationary increments. In \cite{GGL1} we proved a strong uniform approximation with a rate of convergence for fractional Brownian motion by means of transport processes. In this paper we prove a similar type of approximation for sub-fractional Brownian motion.

math.PR↗

arXiv2009

Malliavin calculus for fractional delay equations

In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a Hölder continuous function with parameter greater that 1/2 via the Young integration setting. Then some estimates of the solution are obtained, which allow to show that the solution of a delay differential equation driven by a fractional Brownian motion (fBm) with Hurst parameter H>1/2 has a smooth density. To this purpose, we use Malliavin calculus based on the Frechet differentiability in the directions of the reproducing kernel Hilbert space associated with fBm.

math.PR↗

arXiv2006

Itô's formula for linear fractional PDEs

In this paper we introduce a stochastic integral with respect to the solution X of the fractional heat equation on [0,1], interpreted as a divergence operator. This allows to use the techniques of the Malliavin calculus in order to establish an Itô-type formula for the process X.

math.PR↗

arXiv2006

Linear Stochastic Differential Equations Driven by a Fractional Brownian Motion with Hurst Parameter less than 1/2

In this paper we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here the coefficients are deterministic, the inital condition is anticipating and the underlying fractional Brownian motion has Hurst parameter less than 1/2. We provide an explicit expression for the chaos decomposition of the solution in order to show our results.

math.PR↗