IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v505y2025ics009630032500253x.html

Contractivity of stochastic θ-methods under non-global Lipschitz conditions

Author

Listed:
  • Biščević, Helena
  • D'Ambrosio, Raffaele
  • Di Giovacchino, Stefano

Abstract

The paper is devoted to address the numerical preservation of the exponential mean-square contractive character of the dynamics of stochastic differential equations (SDEs), whose drift and diffusion coefficients are subject to non-global Lipschitz assumptions. The conservative attitude of stochastic θ-methods is analyzed both for Itô and Stratonovich SDEs. The case of systems with linear drift is also analyzed in terms of spectral properties of the coefficient matrix of the drift. Numerical evidence on selected test problems confirms the effectiveness of the approach.

Suggested Citation

  • Biščević, Helena & D'Ambrosio, Raffaele & Di Giovacchino, Stefano, 2025. "Contractivity of stochastic θ-methods under non-global Lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 505(C).
    • Handle: RePEc:eee:apmaco:v:505:y:2025:i:c:s009630032500253x
    DOI: 10.1016/j.amc.2025.129527
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032500253X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129527?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Buckwar, Evelyn & Sickenberger, Thorsten, 2011. "A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1110-1127.
    2. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Liu, Yufen & Cao, Wanrong & Li, Yuelin, 2022. "Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    4. D'Ambrosio, Raffaele & Di Giovacchino, Stefano, 2024. "Strong backward error analysis of symplectic integrators for stochastic Hamiltonian systems," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    5. Tocino, A. & Komori, Y. & Mitsui, T., 2022. "Integration of the stochastic underdamped harmonic oscillator by the θ-method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 217-230.
    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. Mikulevicius, Remigijus & Zhang, Changyong, 2011. "On the rate of convergence of weak Euler approximation for nondegenerate SDEs driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1720-1748, August.
    2. Huang, Hanwen & Huang, Manyu, 2025. "Schrödinger bridge based deep conditional generative learning," Journal of Multivariate Analysis, Elsevier, vol. 210(C).
    3. Rathinasamy, Anandaraman & Nair, Priya, 2018. "Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 276-303.
    4. I. Lubashevsky & M. Hajimahmoodzadeh & A. Katsnelson & P. Wagner, 2003. "Noised-induced phase transition in an oscillatory system with dynamical traps," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 36(1), pages 115-118, November.
    5. Ding-Geng Chen & Haipeng Gao & Chuanshu Ji, 2021. "Bayesian Inference for Stochastic Cusp Catastrophe Model with Partially Observed Data," Mathematics, MDPI, vol. 9(24), pages 1-9, December.
    6. Vargas, Alessandro N. & Caruntu, Constantin F. & Ishihara, João Y. & Bouzahir, Hassane, 2022. "Stochastic stability of switching linear systems with application to an automotive powertrain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 278-287.
    7. de la Cruz, H. & Jimenez, J. C, 2020. "Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    8. Shuaiqiang Liu & Lech A. Grzelak & Cornelis W. Oosterlee, 2022. "The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations," Risks, MDPI, vol. 10(3), pages 1-27, February.
    9. I. A. Lubashevsky & R. Mahnke & M. Hajimahmoodzadeh & A. Katsnelson, 2005. "Long-lived states of oscillator chains with dynamical traps," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(1), pages 63-70, March.
    10. Xueyan Zhao & Feiqi Deng & Shifang Kuang, 2014. "Numerical Schemes for Stochastic Differential Equations with Variable and Distributed Delays: The Interpolation Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    11. Tocino, A. & Zeghdane, R. & Senosiaín, M.J., 2021. "On the MS-stability of predictor–corrector schemes for stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 289-305.
    12. Konakov Valentin & Mammen Enno, 2002. "Edgeworth type expansions for Euler schemes for stochastic differential equations," Monte Carlo Methods and Applications, De Gruyter, vol. 8(3), pages 271-286, December.
    13. Gao, Jianfang & Liang, Hui & Ma, Shufang, 2019. "Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 385-398.
    14. Ranjbar, Hassan, 2025. "Split-step ϑ integrator for generalized stochastic Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 165-186.
    15. K. Maleknejad & M. Khodabin & F. Hosseini Shekarabi, 2014. "Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    16. Kawar Badie Mahmood & Adil Sufian Husain, 2021. "Bernoulli’s Number One Solution for Stochastic Equilibrium," International Journal of Science and Business, IJSAB International, vol. 5(8), pages 194-201.
    17. Schipper, Josh & Bathini, Veerabrahmam & Mukhedkar, Radnya & Watson, Neville & Pirnia, Mehrdad & Nair, Nirmal-Kumar & Watson, Jeremy, 2025. "Steady-state power system analysis revisited for hybrid AC–DC grids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 215(C).
    18. Küchler, Uwe & Platen, Eckhard, 2000. "Strong discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 189-205.
    19. Wei Zhang & Hui Min, 2021. "Weak Convergence Analysis and Improved Error Estimates for Decoupled Forward-Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 9(8), pages 1-15, April.
    20. Bruti-Liberati Nicola & Nikitopoulos-Sklibosios Christina & Platen Eckhard, 2006. "First Order Strong Approximations of Jump Diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 191-209, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:505:y:2025:i:c:s009630032500253x. 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.