Searcharxiv⌕ Search

arXiv subjects

Johanna Garzón

Publications and source records attributed to Johanna Garzón.

6 recordsLinked to original sources
arXiv2026

Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion via Fractional Calculus Techniques

We study a stochastic functional differential equation (SFDE) with memory driven by a fractional Brownian motion (fBm) with Hurst parameter H>1/2. An Euler-type numerical scheme is proposed and analyzed under suitable regularity conditions on the drift and diffusion coefficients using tools from fractional calculus. We prove the convergence of the scheme and derive the corresponding rate in terms of the discretization step. Numerical simulations illustrate the theoretical results and confirm the accuracy of the proposed method.

math.NA↗
arXiv2026

Euler scheme for stochastic functional differential equations driven by fractional Brownian motion

In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic integral is the Young one and the coefficient is evaluated in the set of $λ$-Hölder continuous functions on $[-τ,0]$, for some suitable $τ>0$ and $λ\in(1/2,H)$. The rate of convergence of our scheme is $1/n^γ$, for any $γ<2λ-1$. Also, numerical simulations are provided to illustrate our theoretical results.

math.PR↗
arXiv2026

Optimal extraction with an impact on diffusion-jump pricing

We study an optimal extraction problem where the agent's actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, are evolved by a drifted Brownian motion with jumps. The agent's primary aim is to identify an optimal extraction strategy that maximizes their expected net profits.

math.OC↗
arXiv2021

Gamma mixed fractional Lévy Ornstein-Uhlenbeck process

In this article, we introduce a non Gaussian long memory process constructed by the aggregation of independent copies of a fractional Lévy Ornstein-Uhlenbeck process with random coefficients. Several properties and a limit theorem are studied for this new process. Finally, some simulations of the limit process are shown.

math.PR↗
arXiv2008

Convergence to Weighted Fractional Brownian Sheets

We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values of the parameters the weighted fractional Brownian sheets are obtained as limits in law of occupation time fluctuations of a stochastic particle model. In contrast with some known approximations of fractional Brownian sheets which use a kernel in a Volterra type integral representation of fractional Brownian motion with respect to ordinary Brownian motion, our approximation does not make use of a kernel.

math.PR↗