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Listar por autor "Calatayud Gregori, Julia"

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A full probabilistic solution of the random linear fractional differential equation via the Random Variable Transformation technique

Burgos-Simon, Clara; Calatayud-Gregori, Julia; Cortés, J.-C.; Navarro-Quiles, A. (John Wiley & Sons, 2018)

[EN] This paper provides a full probabilistic solution of the randomized fractional linear nonhomogeneous differential equation with a random initial condition via the computation of the first probability density function ...
A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers' partial differential equation

Calatayud, Julia; Cortés, J.-C.; Jornet, Marc (John Wiley & Sons, 2021-10)

[EN] The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods ...
An introduction to random variables, random vectors and stochastic processes

Calatayud Gregori, Julia; Cortés López, Juan Carlos; Jornet Sanz, Marc; Villanueva Micó, Rafael Jacinto (Editorial Universitat Politècnica de València, 2019-10-01)

This book is aimed at covering the bases on random variables, random vectors and stochastic processes, necessary to be able to address the study of stochastic models based mainly on random and stochastic differential ...
Analysis of the random heat equation via approximate density functions

Calatayud, Julia; Cortés, J.-C. (Editura Academiei Romane, 2021)

[EN] In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coefficient is assumed to be a random variable and the initial condition is treated as a stochastic process. The ...
Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions

Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc (Texas State University. Department of Mathematics, 2019-07-16)

[EN] Solving a random differential equation means to obtain an exact or approximate expression for the solution stochastic process, and to compute its statistical properties, mainly the mean and the variance functions. ...
Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties

Calatayud Gregori, Julia; Cortés, J.-C.; Jornet Sanz, Marc (Taylor & Francis, 2020-09-02)

[EN] In this work, we study the full randomized versions of Airy, Hermite and Laguerre differential equations, which depend on a random variable appearing as an equation coefficient as well as two random initial conditions. ...
Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models

Calatayud-Gregori, Julia; Chen-Charpentier, Benito M.; Cortés, J.C.; Jornet-Sanz, Marc (MDPI AG, 2019-01)

[EN] In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions ...
Computational methods for random differential equations: probability density function and estimation of the parameters

Calatayud Gregori, Julia (Universitat Politècnica de València, 2020-03-05)

[EN] Mathematical models based on deterministic differential equations do not take into account the inherent uncertainty of the physical phenomenon (in a wide sense) under study. In addition, inaccuracies in the collected ...
Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation

Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc (De Gruyter Open, 2018)

[EN] This paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely random non-autonomous second-order linear differential ...
Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC

Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc; Villanueva Micó, Rafael Jacinto (John Wiley & Sons, 2018)

[EN] Population dynamics models consisting of nonlinear difference equations allow us to get a better understanding of the processes involved in epidemiology. Usually, these mathematical models are studied under a deterministic ...
Computing the density function of complex models with randomness by using polynomial expansions and the RVT technique. Application to the SIR epidemic model

Calatayud, Julia; Cortés, J.-C.; Jornet, Marc (Elsevier, 2020-04)

[EN] This paper concerns the computation of the probability density function of the stochastic solution to general complex systems with uncertainties formulated via random differential equations. In the existing literature, ...
Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme

Calatayud, J.; Cortés, J.-C.; Díaz, J.A.; Jornet, M. (Elsevier, 2020-05)

[EN] We study the random heat partial differential equation on a bounded domain assuming that the diffusion coefficient and the boundary conditions are random variables, and the initial condition is a stochastic process. ...
Dealing with variability in ecological modelling: An analysis of a random non-autonomous logistic population model

Calatayud Gregori, Julia; Cortés, J.-C.; Dorini, Fábio A.; Jornet Sanz, Marc (John Wiley & Sons, 2022-04)

[EN] This paper presents a methodology to deal with the randomness associated to ecological modelling. Data variability makes it necessary to analyse the impact of random perturbations on the fitted model parameters. We ...
Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem

Calatayud, J.; Cortés, J.-C.; Díaz, J.A.; Jornet, M. (Taylor & Francis, 2020-05-18)

[EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this ...
Extending the study on the linear advection equation subject to stochastic velocity field and initial condition

Calatayud, J.; Cortés, J.-C.; Dorini, F. A.; Jornet, M. (Elsevier, 2020-06)

[EN] In this paper we extend the study on the linear advection equation with independent stochastic velocity and initial condition performed in Dorini and Cunha (2011). By using both existing and novel results on the ...
Improvement of random coefficient differential models of growth of anaerobic photosynthetic bacteria by combining Bayesian inference and gPC

Calatayud, Julia; Cortés, J.-C.; Jornet, Marc (John Wiley & Sons, 2020-09-30)

[EN] The time evolution of microorganisms, such as bacteria, is of great interest in biology. In the article by D. Stanescu et al. [Electronic Transactions on Numerical Analysis, 34, 44-58 (2009)], a logistic model was ...
Improving the approximation of the first and second order statistics of the response stochastic process to the random Legendre differential equation

Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc (Springer-Verlag, 2019-06)

[EN] In this paper, we deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X-0 and X-1. In a previous study (Calbo et al. in Comput Math Appl ...
Improving the approximation of the probability density function of random nonautonomous logistic-type differential equations

Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc (John Wiley & Sons, 2019-11-19)

[EN] In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P-'(t,omega)=A(t,omega)(1-P(t,omega))P(t,omega), t is an element of[t(0),T], ...
Lp-calculus approach to the random autonomous linear differential equation with discrete delay

Calatayud-Gregori, Julia; Cortés, J.-C.; Jornet-Sanz, Marc (Springer-Verlag, 2019-08)

[EN] In this paper, we provide a full probabilistic study of the random autonomous linear differential equation with discrete delay , with initial condition x(t)=g(t), -t0. The coefficients a and b are assumed to be random ...
Mathematical methods for the randomized non-autonomous Bertalanffy model

Calatayud, Julia; Caraballo, Tomás; Cortés, J.-C.; Jornet, Marc (Texas State University. Department of Mathematics, 2020-05-26)

[EN] In this article we analyze the randomized non-autonomous Bertalanffy model x' (t, omega) = a(t, omega)x(t, omega) b(t, omega)x(t, omega)(2/3), x(t(0), omega) = x(0)(omega), where a(t, omega) and b(t, omega) are ...