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All issues Volume 59 / No 5 (September-October 2025) ESAIM: M2AN, 59 5 (2025) 2329-2348 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
Page(s) 2329 - 2348
DOI https://doi.org/10.1051/m2an/2025061
Published online 17 September 2025
  1. V. Akgiray and G.G. Booth, The stable-law model of stock returns. J. Bus. Econ. Statist. 6 (1988) 51–57. [Google Scholar]
  2. D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd edition. Cambridge University Press, Cambridge (2009). [Google Scholar]
  3. J. Bao, J. Shao and C. Yuan, Approximation of invariant measures for regime-switching diffusions. Potential Anal. 44 (2016) 707–727. [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Bao, G. Yin and C. Yuan, Asymptotic Analysis for Functional Stochastic Differential Equations. Springer Briefs in Mathematics. Springer (2016). [Google Scholar]
  5. I. Bardhan and X. Chao, Pricing options on securities with discontinuous returns. Stoch. Process. Appl. 48 (1993) 123–137. [Google Scholar]
  6. M.E. Caballero, J.C. Pardo and J.L. Pérez-Navero, On Lamperti stable processes. Probab. Math. Statist. 30 (2010) 1–28. [Google Scholar]
  7. Z. Chen, S. Gan and X. Wang, Mean-square approximations of Lévy noise driven SDEs with super-linearly growing diffusion and jump coefficients. Discret. Contin. Dyn. Syst. Ser. B 24 (2019) 4513–4545. [Google Scholar]
  8. Y. Cheng, Y. Hu and H. Long, Generalized moment estimators for α-stable Ornstein–Uhlenbeck motions from discrete observations. Stat. Inference Stoch. Process. 23 (2020) 53–81. [Google Scholar]
  9. R. Cont and P. Tankov, Financial Modelling with Jump Processes, 1st edition. Chapman and Hall/CRC, New York (2004). [Google Scholar]
  10. R. Cont and E. Voltchkova, A finite difference scheme for option pricing in jump diffusion and exponential Lévy models. SIAM J. Numer. Anal. 43 (2005) 1596–1626. [CrossRef] [MathSciNet] [Google Scholar]
  11. K. Dareiotis, C. Kumar and S. Sabanis, On tamed Euler approximations of SDEs driven by Lévy noise with applications to delay equations. SIAM J. Numer. Anal. 54 (2016) 1840–1872. [Google Scholar]
  12. I. Gyöngy and N.V. Krylov, On stochastic equations with respect to semimartingales I. Stochastics 4 (1980) 1–21. [Google Scholar]
  13. D.J. Higham and P.E. Kloeden, Strong convergence rates for backward euler on a class of nonlinear jump-diffusion problems. J. Comput. Appl. Math. 205 (2007) 949–956. [Google Scholar]
  14. X. Huang and Z.-W. Liao, The Euler–Maruyama method for S(F)DEs with Hölder drift and α-stable noise. Stoch. Anal. Appl. 36 (2018) 28–39. [Google Scholar]
  15. X. Huang and F.-F. Yang, Distribution-dependent SDEs with Hölder continuous drift and α-stable noise. Numer. Algorithms 86 (2021) 813–831. [Google Scholar]
  16. M. Hutzenthaler, A. Jentzen and P.E. Kloeden, Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Proc. Roy. Soc. London Ser. A 467 (2011) 1563–1576. [Google Scholar]
  17. Y. Jiang, L. Weng and W. Liu, Stationary distribution of the stochastic theta method for nonlinear stochastic differential equations. Numer. Algorithms 83 (2020) 1531–1553. [Google Scholar]
  18. E. Jum, Numerical approximation of stochastic differential equations driven by Levy motion with infinitely many jumps. Ph.D. thesis, University of Tennessee (2015). [Google Scholar]
  19. U. Küchler and S. Tappe, Tempered stable distributions and processes. Stoch. Process. Appl. 123 (2013) 4256–4293. [Google Scholar]
  20. F. Kühn, Existence and estimates of moments for Lévy-type processes. Stoch. Process. Appl. 127 (2017) 1018–1041. [Google Scholar]
  21. F. Kühn and R.L. Schilling, Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs. Stoch. Process. Appl. 129 (2019) 2654–2680. [Google Scholar]
  22. C. Kumar and S. Sabanis, On tamed milstein schemes of SDEs driven by Lévy noise. Discret. Contin. Dyn. Syst. Ser. B 22 (2017) 421–463. [Google Scholar]
  23. X. Li, X. Mao and G. Yin, Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment and stability. IMA J. Numer. Anal. 39 (2019) 847–892. [Google Scholar]
  24. W. Liu and X. Mao, Numerical stationary distribution and its convergence for nonlinear stochastic differential equations. J. Comput. Appl. Math. 276 (2015) 16–29. [Google Scholar]
  25. W. Liu, X. Mao and Y. Wu, The backward Euler–Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients. Appl. Numer. Math. 184 (2023) 137–150. [Google Scholar]
  26. B.B. Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Springer (1997). [Google Scholar]
  27. X. Mao, Stochastic Differential Equations and Applications, 2nd edition. Elsevier (2008). [Google Scholar]
  28. X. Mao and L. Szpruch, Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients. J. Comput. Appl. Math. 238 (2013) 14–28. [Google Scholar]
  29. F.J. Massey Jr., The Kolmogorov–Smirnov test for goodness of fit. J. Amer. Statist. Assoc. 46 (1951) 68–78. [Google Scholar]
  30. R. Mikulevičius and F. Xu, On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes. Stochastics 90 (2018) 569–604. [Google Scholar]
  31. O.M. Pamen and D. Taguchi, Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient. Stoch. Process. Appl. 127 (2017) 2542–2559. [Google Scholar]
  32. K.-I. Sato, Lévy Processes and Infinitely Divisible Distributions. Vol. 68. Cambridge University Press, Cambridge (1999). [Google Scholar]
  33. D. Talay, Stochastic Hamiltonian systems: exponential convergence to the invariant measure and discretization by the implicit Euler scheme. Markov Process. Relat. Fields 8 (2002) 163–198. [Google Scholar]
  34. J. Tong, X. Jin and Z. Zhang, Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances. Potential Anal. 49 (2018) 503–526. [Google Scholar]
  35. J. Wang, Exponential ergodicity and strong ergodicity for SDEs driven by symmetric α-stable processes. Appl. Math. Lett. 26 (2013) 654–658. [Google Scholar]
  36. W. Zhang, The truncated Euler–Maruyama method for stochastic differential equations with piecewise continuous arguments driven by Lévy noise. Int J. Comput. Math. 98 (2021) 389–413. [Google Scholar]

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