Open Access
Issue |
MATEC Web of Conferences
Volume 362, 2022
XXII International Conference on Computational Mechanics and Modern Applied Software Systems (CMMASS 2021)
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Article Number | 01014 | |
Number of page(s) | 10 | |
DOI | https://doi.org/10.1051/matecconf/202236201014 | |
Published online | 14 September 2022 |
- P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, Berlin, 1995) [Google Scholar]
- E. Platen, N. Bruti-Liberati, Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Springer, Berlin-Heidelberg, 2010) [Google Scholar]
- X. Han, P.E. Kloeden, Random Ordinary Differential Equations and their Numerical Solution (Springer, Singapore, 2017) [Google Scholar]
- Z. Zhang, A. Zeb, S. Hussain, E. Alzahrani, Dynamics of COVID-19 mathematical model with stochastic perturbation, Adv. Differ. Equ., 451 (2020), DOI: 10.1186/S13662-020-02909-1 [CrossRef] [Google Scholar]
- A. Alzahrani, A. Zeb, Detectable sensation of a stochastic smoking model, Open Math., 18, 1045 (2020), DOI: 10.1515/math-2020-0068 [CrossRef] [Google Scholar]
- G. Li, Y. Liu, The dynamics of a stochastic SIR epidemic model with nonlinear incidence and vertical transmission, Discr. Dyn. Nat. Soc., 2021, 4645203 (2021), DOI: 10.1155/2021/4645203 [Google Scholar]
- Y. Jiao, C. Ma, S. Scotti, C. Zhou, The Alpha-Heston stochastic volatility model, Math. Finance, 31(3), 943 (2021), DOI: 10.1111/mafi.12306 [CrossRef] [Google Scholar]
- G.N. Milstein, Numerical Integration of Stochastic Differential Equations (Ural University Press, Sverdlovsk, 1988) [Google Scholar]
- G.N. Milstein, M.V. Tretyakov, Stochastic Numerics for Mathematical Physics (Springer, Berlin, 2004) [Google Scholar]
- D.F. Kuznetsov, Numerical Integration of Stochastic Differential Equations 2 (Polytechnical University Publishing House, Saint-Petersburg, 2006), DOI: 10.18720/SPBPU/2/s17-227 [Google Scholar]
- D.F. Kuznetsov, M.D. Kuznetsov, Optimization of the mean-square approximation procedures for iterated Ito stochastic integrals based on multiple Fourier-Legendre series, J. Phys.: Conf. Ser., 1925, 012010 (2021), DOI: 10.1088/1742-6596/1925/1/012010 [CrossRef] [Google Scholar]
- D.F. Kuznetsov, Strong approximation of iterated Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Application to numerical solution of Ito SDEs and semilinear SPDEs, arXiv:2003.14184v27 [math.PR], 1–869 (2022), DOI: 10.48550/arXiv.2003.14184 [Google Scholar]
- P.E. Kloeden, E. Platen, I.W. Wright, The approximation of multiple stochastic integrals, Stoch. Anal. Appl., 10(4), 431 (1992), DOI: 10.1080/07362999208809281 [CrossRef] [Google Scholar]
- J.G. Gaines, T.J. Lyons, Random generation of stochastic area integrals, SIAM J. Appl. Math., 54, 1132(1994), DOI: 10.1137/S0036139992235706 [CrossRef] [Google Scholar]
- T.A. Averina, S.M. Prigarin, Calculation of stochastic integrals of Wiener processes (Inst. Comp. Math. Math. Geophys. Siberian Branch Russ. Acad. Sci., Novosibirsk), Preprint 1048, 1–15 (1995) [Google Scholar]
- C.W. Li, X.Q. Liu, Approximation of multiple stochastic integrals and its application to stochastic differential equations, Nonlinear Anal. Theor. Meth. Appl., 30(2), 697 (1997), DOI: 10.1016/S0362-546X(96)00253-2 [CrossRef] [Google Scholar]
- S.M. Prigarin, S.M. Belov, One application of series expansions of Wiener process (Inst. Comp. Math. Math. Geophys. Siberian Branch Russ. Acad. Sci., Novosibirsk), Preprint 1107, 1–16(1998) [Google Scholar]
- M. Wiktorsson, Joint characteristic function and simultaneous simulation of iterated Ito integrals for multiple independent Brownian motions, Ann. Appl. Prob., 11(2), 470 (2001), DOI: 10.1214/aoap/1015345301 [CrossRef] [Google Scholar]
- T. Ryden, M. Wiktorsson, On the simulation of iterated Ito integrals, Stoch. Proc. Appl., 91(1), 151 (2001), DOI: 10.1016/S0304-4149(00)00053-3 [CrossRef] [Google Scholar]
- E. Allen, Approximation of triple stochastic integrals through region subdivision, Commun. Appl. Analysis., 17, 355 (2013) [Google Scholar]
- X. Tang, A. Xiao, Asymptotically optimal approximation of some stochastic integrals and its applications to the strong second-order methods, Adv. Comp. Math., 45, 813 (2019), DOI: 10.1007/s10444-018-9638-0 [CrossRef] [Google Scholar]
- K.A. Rybakov, Using spectral form of mathematical description to represent iterated Stratonovich stochastic integrals, in Applied Mathematics and Computational Mechanics for Smart Applications. Smart Innovation, Systems and Technologies, vol. 217, ed. by L.C. Jain, M.N. Favorskaya, I.S. Nikitin, D.L. Reviznikov (Springer, Singapore, 2021), pp. 287–304, DOI: 10.1007/978-981-33-4826-4_20 [CrossRef] [Google Scholar]
- M.D. Kuznetsov, D.F. Kuznetsov, SDE-MATH: A software package for the implementation of strong high-order numerical methods for Ito SDEs with multidimensional non-commutative noise based on multiple Fourier-Legendre, Differential Equations and Control Processes, 1, 93 (2021), URL https://diffjournal.spbu.ru/EN/numbers/2021.1/article.1.5.html [Google Scholar]
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