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Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients

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  • Liu, Yufen
  • Cao, Wanrong
  • Li, Yuelin

Abstract

In this paper, a split-step balanced θ-method (SSBT) has been presented for solving stochastic differential equations (SDEs) under non-global Lipschitz conditions, where θ∈[0,1] is a parameter of the scheme. The moment boundedness and strong convergence of the numerical solution have been studied, and the convergence rate is 0.5. Moreover, under some conditions it is proved that the SSBT scheme can preserve the exponential mean-square stability of the exact solution when θ∈(1/2,1] for every step size h>0. Numerical examples verify the theoretical findings.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321005269
    DOI: 10.1016/j.amc.2021.126437
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    References listed on IDEAS

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    1. Yao, Jinran & Gan, Siqing, 2018. "Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 294-301.
    2. G. N. Milstein & Eckhard Platen & H. Schurz, 1998. "Balanced Implicit Methods for Stiff Stochastic Systems," Published Paper Series 1998-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    3. Liu, Linna & Deng, Feiqi & Hou, Ting, 2018. "Almost sure exponential stability of implicit numerical solution for stochastic functional differential equation with extended polynomial growth condition," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 201-212.
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    1. 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).
    2. 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.

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