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An Introduction to Numerical Methods for Stochastic Differential Equations

Citations

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Cited by:

  1. 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.
  2. 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.
  3. 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.
  4. Hausenblas Erika, 2000. "Momte Carlo Simulation of killed diffusion," Monte Carlo Methods and Applications, De Gruyter, vol. 6(4), pages 263-296, December.
  5. 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).
  6. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, March.
  7. 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.
  8. 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.
  9. Borghi, Giacomo & Grassi, Sara & Pareschi, Lorenzo, 2023. "Consensus based optimization with memory effects: Random selection and applications," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
  10. Huang, Hanwen & Huang, Manyu, 2025. "Schrödinger bridge based deep conditional generative learning," Journal of Multivariate Analysis, Elsevier, vol. 210(C).
  11. 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.
  12. 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.
  13. 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.
  14. 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).
  15. Miccichè, S., 2023. "A numerical recipe for the computation of stationary stochastic processes’ autocorrelation function," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
  16. 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).
  17. 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.
  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. 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.
  20. 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.
  21. 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).
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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).
  28. 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.
  29. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
  30. 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.
  31. 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.
  32. 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.
  33. Dylan Herman & Yue Sun & Jin-Peng Liu & Marco Pistoia & Charlie Che & Rob Otter & Shouvanik Chakrabarti & Aram Harrow, 2026. "Quantum Speedups for Derivative Pricing Beyond Black-Scholes," Papers 2602.03725, arXiv.org.
  34. 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.
  35. 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.
  36. Anna Knezevic, 2024. "Enhancing path-integral approximation for non-linear diffusion with neural network," Papers 2404.08903, arXiv.org.
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