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Johanna Garzon

Publications and source records attributed to Johanna Garzon.

3 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↗