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First-passage-time location function: Application to determine first-passage-time densities in diffusion processes

Author

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  • Román, P.
  • Serrano, J.J.
  • Torres, F.

Abstract

A time-dependent function, namely the First-Passage-Time Location function, is introduced in the context of the study of first-passage-times. From this function, a strategy is developed in order to solve numerically the Volterra integral equation of the second kind verified by the first-passage-time densities for diffusion processes. The proposed procedure provides the advantages in the application of quadrature methods in terms of an appropriate choice of the integration step, as well as an outstanding reduction in the computational cost. Some examples are developed showing the validity of that strategy as well as the computational advantages.

Suggested Citation

  • Román, P. & Serrano, J.J. & Torres, F., 2008. "First-passage-time location function: Application to determine first-passage-time densities in diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4132-4146, April.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:8:p:4132-4146
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    Cited by:

    1. Patricia Román-Román & Sergio Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Using First-Passage Times to Analyze Tumor Growth Delay," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    2. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    3. Antonio Barrera & Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic," Mathematics, MDPI, vol. 9(19), pages 1-29, September.
    4. Antonio Di Crescenzo & Paola Paraggio & Patricia Román-Román & Francisco Torres-Ruiz, 2023. "Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean," Statistical Papers, Springer, vol. 64(5), pages 1391-1438, October.

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