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An Introduction to Numerical Methods for Stochastic Differential Equations

Citations

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Cited by:

  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. Ganguly, Arnab & Sundar, P., 2021. "Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 74-110.
  3. 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.
  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. 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.
  6. Xu Liao & Lican Kang & Yihao Peng & Xiaoran Chai & Peng Xie & Chengqi Lin & Hongkai Ji & Yuling Jiao & Jin Liu, 2024. "Multivariate stochastic modeling for transcriptional dynamics with cell-specific latent time using SDEvelo," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
  7. Yuan, Haiyan & Zhu, Quanxin, 2024. "Practical stability of the analytical and numerical solutions of stochastic delay differential equations driven by G-Brownian motion via some novel techniques," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
  8. 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.
  9. Remigijus Mikulevičius & Changyong Zhang, 2024. "Convergence of Weak Euler Approximation for Nondegenerate Stochastic Differential Equations Driven by Point and Martingale Measures," Journal of Theoretical Probability, Springer, vol. 37(1), pages 43-80, March.
  10. Gao, Jiti, 2002. "Modeling long-range dependent Gaussian processes with application in continuous-time financial models," MPRA Paper 11973, University Library of Munich, Germany, revised 18 Sep 2003.
  11. 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.
  12. Kubilius Kestutis & Platen Eckhard, 2002. "Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps," Monte Carlo Methods and Applications, De Gruyter, vol. 8(1), pages 83-96, December.
  13. 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.
  14. Küchler, Uwe & Platen, Eckhard, 2002. "Weak discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 497-507.
  15. 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.
  16. 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).
  17. 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.
  18. Mikulevicius, R., 2012. "On the rate of convergence of simple and jump-adapted weak Euler schemes for Lévy driven SDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2730-2757.
  19. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
  20. Hausenblas Erika, 2000. "Momte Carlo Simulation of killed diffusion," Monte Carlo Methods and Applications, De Gruyter, vol. 6(4), pages 263-296, December.
  21. Shuaiqiang Liu & Graziana Colonna & Lech A. Grzelak & Cornelis W. Oosterlee, 2023. "GPU acceleration of the Seven-League Scheme for large time step simulations of stochastic differential equations," Papers 2302.05170, arXiv.org.
  22. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2007, January-A.
  23. A. S. Hurn & K. A. Lindsay & V. L. Martin, 2003. "On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 45-63, January.
  24. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, December.
  25. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
  26. Kamrani, Minoo & Hosseini, S. Mohammad, 2012. "Spectral collocation method for stochastic Burgers equation driven by additive noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1630-1644.
  27. Borghi, Giacomo & Grassi, Sara & Pareschi, Lorenzo, 2023. "Consensus based optimization with memory effects: Random selection and applications," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
  28. Huang, Hanwen & Huang, Manyu, 2025. "Schrödinger bridge based deep conditional generative learning," Journal of Multivariate Analysis, Elsevier, vol. 210(C).
  29. 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.
  30. Anna Knezevic, 2024. "Enhancing path-integral approximation for non-linear diffusion with neural network," Papers 2404.08903, arXiv.org.
  31. 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.
  32. 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.
  33. Miccichè, S., 2023. "A numerical recipe for the computation of stationary stochastic processes’ autocorrelation function," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
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