IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v451y2023ics0096300323001819.html
   My bibliography  Save this article

On a time-inhomogeneous diffusion process with discontinuous drift

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323001819
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Huang, Jianlin & Golubović, Dušan S & Koh, Sau & Yang, Daoguo & Li, Xiupeng & Fan, Xuejun & Zhang, G.Q., 2016. "Lumen degradation modeling of white-light LEDs in step stress accelerated degradation test," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 152-159.
    3. Kulmus, Kathrin & Essex, Christopher & Prehl, Janett & Hoffmann, Karl Heinz, 2019. "The entropy production paradox for fractional master equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1370-1378.
    4. Polotto, Franciele & Drigo Filho, Elso & Chahine, Jorge & Oliveira, Ronaldo Junio de, 2018. "Supersymmetric quantum mechanics method for the Fokker–Planck equation with applications to protein folding dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 286-300.
    5. Hu, Changhua & Xing, Yuanxing & Du, Dangbo & Si, Xiaosheng & Zhang, Jianxun, 2023. "Remaining useful life estimation for two-phase nonlinear degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    6. Zhang, Jian-Xun & Du, Dang-Bo & Si, Xiao-Sheng & Hu, Chang-Hua & Zhang, Han-Wen, 2021. "Joint optimization of preventive maintenance and inventory management for standby systems with hybrid-deteriorating spare parts," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    7. Satin, Y.A. & Razumchik, R.V. & Zeifman, A.I. & Kovalev, I.A., 2022. "Upper bound on the rate of convergence and truncation bound for non-homogeneous birth and death processes on Z," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    8. Zheng, Jianfei & Ren, Jincheng & Zhang, Jianxun & Pei, Hong & Zhang, Zhengxin, 2023. "A lifetime prediction method for Lithium-ion batteries considering storage degradation of spare parts," Energy, Elsevier, vol. 282(C).
    9. Rytis Kazakeviv{c}ius & Aleksejus Kononovicius, 2023. "Anomalous diffusion and long-range memory in the scaled voter model," Papers 2301.08088, arXiv.org, revised Feb 2023.
    10. Guo, Jingbo & Wang, Changxi & Cabrera, Javier & Elsayed, Elsayed A., 2018. "Improved inverse Gaussian process and bootstrap: Degradation and reliability metrics," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 269-277.
    11. 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.
    12. Philipp, Lucas & Shizgal, Bernie D., 2019. "A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 158-166.
    13. David Scott Hunter & Ajay Saini & Tauhid Zaman, 2017. "Picking Winners: A Data Driven Approach to Evaluating the Quality of Startup Companies," Papers 1706.04229, arXiv.org, revised Jul 2018.
    14. Correale, T.G. & Monteiro, L.H.A., 2016. "On the dynamics of axonal membrane: Ion channel as the basic unit of a deterministic model," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 292-302.
    15. V. V. Ryazanov, 2021. "First-passage time and change of entropy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(12), pages 1-19, December.
    16. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    17. Qinglai Dong & Lirong Cui, 2019. "First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 1-23, March.
    18. Rui, Weiguo & Yang, Xinsong & Chen, Fen, 2022. "Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    19. Heng-Li Liu & Quan-Lin Li, 2023. "Matched Queues with Flexible and Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    20. Zhiyong Jin & Liqun Wang, 2017. "First Passage Time for Brownian Motion and Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 237-253, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:451:y:2023:i:c:s0096300323001819. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.