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A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm.

Antonio Barrera1, Patricia Román-Román2, Francisco Torres-Ruiz2

  • 1Departamento de Matemática Aplicada, E.T.S.I. Informática, Bulevar Louis Pasteur, 35, Campus de Teatinos, Universidad de Málaga, 29071 Málaga, Spain.

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Summary
This summary is machine-generated.

This study introduces a new stochastic diffusion process with a hyperbolastic mean. The firefly algorithm is used for parameter estimation, demonstrating effectiveness with simulated and real data.

Keywords:
Diffusion processFirefly algorithmHyperbolastic curve

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Area of Science:

  • Stochastic processes
  • Mathematical modeling
  • Statistical inference

Background:

  • Stochastic diffusion processes are fundamental in modeling dynamic systems.
  • Hyperbolastic curves offer unique functional forms for describing growth or decay patterns.
  • Parameter estimation in complex stochastic models remains a significant challenge.

Purpose of the Study:

  • To present a novel stochastic diffusion process characterized by a type I hyperbolastic mean function.
  • To investigate the fundamental properties and behaviors of this new process.
  • To address the challenge of parameter estimation for this model using advanced optimization techniques.

Main Methods:

  • Development of a stochastic diffusion process with a type I hyperbolastic mean.
  • Analysis of the process's main characteristics.
  • Application of the firefly metaheuristic optimization algorithm for maximum likelihood estimation.
  • Implementation of a stagewise procedure to bound the parametric space prior to optimization.

Main Results:

  • The study successfully defines and characterizes the proposed stochastic diffusion process.
  • The firefly algorithm, combined with stagewise bounding, proves effective for parameter estimation.
  • Illustrative examples using both simulated sample paths and real-world data validate the methodology.

Conclusions:

  • The presented stochastic diffusion process with a type I hyperbolastic mean offers a viable new tool for modeling.
  • The proposed maximum likelihood estimation method using the firefly algorithm is robust and practical.
  • The findings are applicable to diverse fields requiring the analysis of such dynamic processes.