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On a time-inhomogeneous diffusion process with discontinuous drift

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  • Giorno, Virginia
  • Nobile, Amelia G.

Abstract

We start from a time-inhomogeneous diffusion process, obtained by applying the composition method to two Wiener processes. Then, we investigate the corresponding diffusion process, restricted by a reflecting boundary in the zero-state. Moreover, we consider a special time-inhomogeneous diffusion process symmetric with respect to zero-state characterized by discontinuous drift. Various numerical computations are performed in the presence of periodic noise intensity.

Suggested Citation

  • Giorno, Virginia & Nobile, Amelia G., 2023. "On a time-inhomogeneous diffusion process with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    • Handle: RePEc:eee:apmaco:v:451:y:2023:i:c:s0096300323001819
    DOI: 10.1016/j.amc.2023.128012
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    References listed on IDEAS

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    1. Molini, A. & Talkner, P. & Katul, G.G. & Porporato, A., 2011. "First passage time statistics of Brownian motion with purely time dependent drift and diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1841-1852.
    2. Antonio Di Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2018. "A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation," Mathematics, MDPI, vol. 6(5), pages 1-23, May.
    3. Caldas, Denise & Chahine, Jorge & Filho, Elso Drigo, 2014. "The Fokker–Planck equation for a bistable potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 92-100.
    4. Itai Benjamini & Susan Lee, 1997. "Conditioned Diffusions which are Brownian Bridges," Journal of Theoretical Probability, Springer, vol. 10(3), pages 733-736, July.
    5. Buonocore, A. & Nobile, A.G. & Pirozzi, E., 2018. "Generating random variates from PDF of Gauss–Markov processes with a reflecting boundary," Computational Statistics & Data Analysis, Elsevier, vol. 118(C), pages 40-53.
    6. Giorno, Virginia & Nobile, Amelia G., 2020. "On a class of birth-death processes with time-varying intensity functions," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    7. Virginia Giorno & Amelia G. Nobile, 2019. "Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions," Mathematics, MDPI, vol. 7(6), pages 1-19, June.
    8. Buonocore, A. & Caputo, L. & Nobile, A.G. & Pirozzi, E., 2014. "Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 799-809.
    9. Virginia Giorno & Amelia G. Nobile, 2021. "On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes," Mathematics, MDPI, vol. 9(8), pages 1-25, April.
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