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An Introduction to Numerical Methods for Stochastic Differential Equations

Citations

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Cited by:

  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. Hausenblas Erika, 2000. "Momte Carlo Simulation of killed diffusion," Monte Carlo Methods and Applications, De Gruyter, vol. 6(4), pages 263-296, December.
  3. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, October.
  4. 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.
  5. 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.
  6. Borghi, Giacomo & Grassi, Sara & Pareschi, Lorenzo, 2023. "Consensus based optimization with memory effects: Random selection and applications," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Miccichè, S., 2023. "A numerical recipe for the computation of stationary stochastic processes’ autocorrelation function," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. Anna Knezevic, 2024. "Enhancing path-integral approximation for non-linear diffusion with neural network," Papers 2404.08903, arXiv.org.
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