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Addendum: Shqair, M., et al. Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method. Mathematics 2019, 7, 633
Open AccessArticle

Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

1
Department of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, 26100 Berrechid, Morocco
2
Department of Statistics and Operational Research, Facultad de Ciencias, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(11), 1062; https://doi.org/10.3390/math7111062
Received: 16 July 2019 / Revised: 26 August 2019 / Accepted: 27 August 2019 / Published: 6 November 2019
(This article belongs to the Section Mathematics and Computers Science)
In this paper, we study the one-dimensional homogeneous stochastic Brennan–Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial mathematics, for example in deriving a numerical model for convertible bond prices. In this work, we obtain the probabilistic characteristics of the process such as the analytical expression, the trend functions (conditional and non-conditional), and the stationary distribution of the model. We also establish a methodology for the estimation of the parameters in the process: First, we estimate the drift parameters by the maximum likelihood approach, with continuous sampling. Then, we estimate the diffusion coefficient by a numerical approximation. Finally, to evaluate the capability of this process for modeling real data, we applied the stochastic Brennan–Schwartz diffusion process to study the evolution of electricity net consumption in Morocco. View Full-Text
Keywords: Brennan–Schwartz diffusion model; stochastic differential equation; inference in diffusion processes; stationary distribution; application; electricity net consumption in Morocco Brennan–Schwartz diffusion model; stochastic differential equation; inference in diffusion processes; stationary distribution; application; electricity net consumption in Morocco
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MDPI and ACS Style

Nafidi, A.; Moutabir, G.; Gutiérrez-Sánchez, R. Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application. Mathematics 2019, 7, 1062.

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