IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i17p3755-d1230339.html
   My bibliography  Save this article

Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts

Author

Listed:
  • Maryam Siddiqui

    (Department of Mathematics, College of Science, King Saud University (KSU), P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Mhamed Eddahbi

    (Department of Mathematics, College of Science, King Saud University (KSU), P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Omar Kebiri

    (Department of Stochastics and Its Applications, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, 01968 Senftenberg, Germany)

Abstract

This paper deals with numerical analysis of solutions to stochastic differential equations with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic real-valued function that satisfies a second-order differential equation. The Euler–Maruyama scheme is used to approximate the solution to the equations. It is shown that the rate of convergence is 1 2 . Numerically, two different methods are used to approximate solutions for this class of SDEJs. The first method is the direct approximation of the original equation using the Euler–Maruyama scheme with specific tests for the evaluation of the singular part at simulated values of the solution. The second method consists of taking the inverse of the Euler–Maruyama approximation for Zvonkin’s transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical methods is carried out. Theoretical results are illustrated and proved by means of an example.

Suggested Citation

  • Maryam Siddiqui & Mhamed Eddahbi & Omar Kebiri, 2023. "Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts," Mathematics, MDPI, vol. 11(17), pages 1-14, August.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3755-:d:1230339
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/17/3755/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/17/3755/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ioannis Lestas & Glenn Vinnicombe & Johan Paulsson, 2010. "Fundamental limits on the suppression of molecular fluctuations," Nature, Nature, vol. 467(7312), pages 174-178, September.
    2. Pellegrini, Clément, 2010. "Existence, uniqueness and approximation of the jump-type stochastic Schrodinger equation for two-level systems," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1722-1747, August.
    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. Michael Chevalier & Ophelia Venturelli & Hana El-Samad, 2015. "The Impact of Different Sources of Fluctuations on Mutual Information in Biochemical Networks," PLOS Computational Biology, Public Library of Science, vol. 11(10), pages 1-21, October.
    2. Luca Cardelli & Rosa D Hernansaiz-Ballesteros & Neil Dalchau & Attila Csikász-Nagy, 2017. "Efficient Switches in Biology and Computer Science," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-16, January.
    3. Christopher C Govern & Arup K Chakraborty, 2013. "Stochastic Responses May Allow Genetically Diverse Cell Populations to Optimize Performance with Simpler Signaling Networks," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-9, August.
    4. Angélique Richard & Loïs Boullu & Ulysse Herbach & Arnaud Bonnafoux & Valérie Morin & Elodie Vallin & Anissa Guillemin & Nan Papili Gao & Rudiyanto Gunawan & Jérémie Cosette & Ophélie Arnaud & Jean-Ja, 2016. "Single-Cell-Based Analysis Highlights a Surge in Cell-to-Cell Molecular Variability Preceding Irreversible Commitment in a Differentiation Process," PLOS Biology, Public Library of Science, vol. 14(12), pages 1-35, December.
    5. Christoph Zechner & Heinz Koeppl, 2014. "Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-9, December.

    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:gam:jmathe:v:11:y:2023:i:17:p:3755-:d:1230339. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.