Bréhier, Charles-Edouard Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime. (English) Zbl 1532.65007 J. Comput. Dyn. 11, No. 2, 189-219 (2024). MSC: 65C30 60H35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ye, Felix X.-F.; Yang, Sichen; Maggioni, Mauro Nonlinear model reduction for slow-fast stochastic systems near unknown invariant manifolds. (English) Zbl 1533.37117 J. Nonlinear Sci. 34, No. 1, Paper No. 22, 54 p. (2024). MSC: 37H30 60H10 60H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bréhier, Charles-Edouard Uniform strong and weak error estimates for numerical schemes applied to multiscale SDEs in a Smoluchowski-Kramers diffusion approximation regime. (English) Zbl 1545.65028 J. Comput. Dyn. 10, No. 3, 387-424 (2023). MSC: 65C30 60H10 60H35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Ruifang; Xu, Yong; Pei, Bin Stochastic averaging for a completely integrable Hamiltonian system with fractional Brownian motion. (English) Zbl 1535.60068 Stoch. Dyn. 23, No. 4, Article ID 2350026, 23 p. (2023). MSC: 60G22 60H10 34C29 37J35 × Cite Format Result Cite Review PDF Full Text: DOI
Yuan, Mingxia; Wang, Bingjun; Yang, Zhiyan On the averaging principle for stochastic differential equations driven by \(G\)-Lévy process. (English) Zbl 1515.60172 Stat. Probab. Lett. 195, Article ID 109789, 8 p. (2023). MSC: 60H05 60H10 60G65 × Cite Format Result Cite Review PDF Full Text: DOI
Sun, Xiaobin; Xie, Yingchao Orders of strong and weak averaging principle for multi-scale SPDEs driven by \(\alpha \)-stable process. (English) Zbl 1512.60042 J. Differ. Equations 351, 194-242 (2023). Reviewer: Martin Ondreját (Praha) MSC: 60H15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Ruifang; Xu, Yong; Pei, Bin Stochastic averaging for a type of fractional differential equations with multiplicative fractional Brownian motion. (English) Zbl 07880329 Chaos 32, No. 12, Article ID 123135, 7 p. (2022). MSC: 37-XX 34-XX × Cite Format Result Cite Review PDF Full Text: DOI
Jiang, Tao; Liu, Yancai Averaging principle for two-time-scale stochastic differential equations with correlated noise. (English) Zbl 1503.34108 Open Math. 20, 1656-1664 (2022). MSC: 34F05 60H10 34C29 × Cite Format Result Cite Review PDF Full Text: DOI
Abdulle, Assyr; Rosilho de Souza, Giacomo Explicit stabilized multirate method for stiff stochastic differential equations. (English) Zbl 1491.60115 SIAM J. Sci. Comput. 44, No. 4, A1859-A1883 (2022). MSC: 60H35 65C20 65C30 65L04 65L06 65L20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xu, Jie An averaging principle for slow-fast fractional stochastic parabolic equations on unbounded domains. (English) Zbl 1497.60091 Stochastic Processes Appl. 150, 358-396 (2022). Reviewer: Dejun Luo (Beijing) MSC: 60H15 35R11 70K65 70K70 × Cite Format Result Cite Review PDF Full Text: DOI
Garnier, Josselin; Mertz, Laurent A control variate method driven by diffusion approximation. (English) Zbl 1489.93118 Commun. Pure Appl. Math. 75, No. 3, 455-492 (2022). MSC: 93E03 93C15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bréhier, Charles-Edouard; Rakotonirina-Ricquebourg, Shmuel On asymptotic preserving schemes for a class of stochastic differential equations in averaging and diffusion approximation regimes. (English) Zbl 1481.65019 Multiscale Model. Simul. 20, No. 1, 118-163 (2022). MSC: 65C30 60H35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hong, Wei; Li, Shihu; Liu, Wei Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs. (English) Zbl 1487.60123 J. Differ. Equations 316, 94-135 (2022). Reviewer: David Prömel (Mannheim) MSC: 60H15 35R60 70K70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xu, Yong; Yang, Xiaoyu; Pei, Bin; Bai, Yuzhen Convergence of martingale solutions to the hybrid slow-fast system. (English) Zbl 1513.70082 J. Eng. Math. 132, Paper No. 20, 15 p. (2022). MSC: 70K70 60J25 60G51 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sun, Xiaobin; Xie, Longjie; Xie, Yingchao Strong and weak convergence rates for slow-fast stochastic differential equations driven by \(\alpha \)-stable process. (English) Zbl 1494.60068 Bernoulli 28, No. 1, 343-369 (2022). MSC: 60H10 60H20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Liu, Jiankang; Xu, Wei; Guo, Qin Averaging principle for impulsive stochastic partial differential equations. (English) Zbl 1475.60122 Stoch. Dyn. 21, No. 4, Article ID 2150014, 19 p. (2021). MSC: 60H15 37L55 34A37 37A50 74H10 × Cite Format Result Cite Review PDF Full Text: DOI
Röckner, Michael; Sun, Xiaobin; Xie, Yingchao Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations. (English. French summary) Zbl 1491.60088 Ann. Inst. Henri Poincaré, Probab. Stat. 57, No. 1, 547-576 (2021). MSC: 60H10 34F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Maclean, John; Bunder, J. E.; Roberts, A. J. A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation. (English) Zbl 1472.65175 Numer. Algorithms 87, No. 4, 1729-1748 (2021). MSC: 65Y15 65-04 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xu, Wenjing; Xu, Wei; Lu, Kai An averaging principle for stochastic differential equations of fractional order \(0 < \alpha < 1\). (English) Zbl 1474.60168 Fract. Calc. Appl. Anal. 23, No. 3, 908-919 (2020). MSC: 60H15 35R11 × Cite Format Result Cite Review PDF Full Text: DOI
Sun, Xiaobin; Zhai, Jianliang Averaging principle for stochastic real Ginzburg-Landau equation driven by \(\alpha\)-stable process. (English) Zbl 1431.35259 Commun. Pure Appl. Anal. 19, No. 3, 1291-1319 (2020). MSC: 35R60 60H15 35Q56 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Shihu; Xie, Yingchao Averaging principle for stochastic 3D fractional Leray-\(\alpha\) model with a fast oscillation. (English) Zbl 1447.60109 Stochastic Anal. Appl. 38, No. 2, 248-276 (2020). MSC: 60H15 70K70 35Q30 35R60 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Wei; Röckner, Michael; Sun, Xiaobin; Xie, Yingchao Averaging principle for slow-fast stochastic differential equations with time dependent locally Lipschitz coefficients. (English) Zbl 1448.60124 J. Differ. Equations 268, No. 6, 2910-2948 (2020). MSC: 60H10 34K33 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wen, Jiaping \(L^{p}\) (\(p>2\))-strong convergence of multiscale integration scheme for jump-diffusion systems. (English) Zbl 1458.65010 Adv. Difference Equ. 2019, Paper No. 20, 20 p. (2019). MSC: 65C30 60H10 34F05 × Cite Format Result Cite Review PDF Full Text: DOI
Lu, Jianfeng; Spiliopoulos, Konstantinos Analysis of multiscale integrators for multiple attractors and irreversible Langevin samplers. (English) Zbl 1409.65006 Multiscale Model. Simul. 16, No. 4, 1859-1883 (2018). MSC: 65C30 60H10 60H35 65L04 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gao, Peng Averaging principle for the higher order nonlinear Schrödinger equation with a random fast oscillation. (English) Zbl 1394.35473 J. Stat. Phys. 171, No. 5, 897-926 (2018). MSC: 35Q55 35Q53 60H15 70K65 70K70 35R60 × Cite Format Result Cite Review PDF Full Text: DOI
Fu, Hongbo; Wan, Li; Liu, Jicheng; Liu, Xianming Weak order in averaging principle for stochastic wave equation with a fast oscillation. (English) Zbl 1396.60074 Stochastic Processes Appl. 128, No. 8, 2557-2580 (2018). MSC: 60H15 60H10 35R60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xu, Jie \(L^{p}\)-strong convergence of the averaging principle for slow-fast SPDEs with jumps. (English) Zbl 1348.60095 J. Math. Anal. Appl. 445, No. 1, 342-373 (2017). MSC: 60H15 60J75 60G57 60F15 × Cite Format Result Cite Review PDF Full Text: DOI
Mao, Wei; Mao, Xuerong An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure. (English) Zbl 1419.60046 Adv. Difference Equ. 2016, Paper No. 77, 18 p. (2016). MSC: 60H10 34K50 34K40 60H20 65C30 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Jie; Miao, Yu; Liu, Jicheng Strong averaging principle for two-time-scale non-autonomous stochastic FitzHugh-Nagumo system with jumps. (English) Zbl 1366.60088 J. Math. Phys. 57, No. 9, 092704, 21 p. (2016). MSC: 60H15 × Cite Format Result Cite Review PDF Full Text: DOI
Mao, Wei; You, Surong; Wu, Xiaoqian; Mao, Xuerong On the averaging principle for stochastic delay differential equations with jumps. (English) Zbl 1346.60087 Adv. Difference Equ. 2015, Paper No. 70, 19 p. (2015). MSC: 60H10 60F25 60F05 60G57 34K50 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Jie; Miao, Yu \(L^p(p > 2)\)-strong convergence of an averaging principle for two-time-scales jump-diffusion stochastic differential equations. (English) Zbl 1384.34070 Nonlinear Anal., Hybrid Syst. 18, 33-47 (2015). Reviewer: Romeo Negrea (Timişoara) MSC: 34F05 34C29 34E15 60J75 60H20 × Cite Format Result Cite Review PDF Full Text: DOI
Maclean, John A note on implementations of the boosting algorithm and heterogeneous multiscale methods. (English) Zbl 1326.65084 SIAM J. Numer. Anal. 53, No. 5, 2472-2487 (2015). MSC: 65L04 34E13 65L05 34A34 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Maclean, John; Gottwald, Georg A. On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations. (English) Zbl 1320.65107 J. Comput. Appl. Math. 288, 44-69 (2015). MSC: 65L04 34E13 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Fu, Hongbo; Wan, Li; Liu, Jicheng Strong convergence in averaging principle for stochastic hyperbolic-parabolic equations with two time-scales. (English) Zbl 1322.60111 Stochastic Processes Appl. 125, No. 8, 3255-3279 (2015). MSC: 60H15 60F15 70K70 × Cite Format Result Cite Review PDF Full Text: DOI
Fu, Hongbo; Wan, Li; Wang, Youzhen; Liu, Jicheng Strong convergence rate in averaging principle for stochastic FitzHugh-Nagumo system with two time-scales. (English) Zbl 1325.60107 J. Math. Anal. Appl. 416, No. 2, 609-628 (2014). MSC: 60H15 60H10 60F15 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Di Strong convergence rate of principle of averaging for jump-diffusion processes. (English) Zbl 1255.60098 Front. Math. China 7, No. 2, 305-320 (2012). MSC: 60H10 70K65 × Cite Format Result Cite Review PDF Full Text: DOI
Fu, Hongbo; Liu, Jicheng Strong convergence in stochastic averaging principle for two time-scales stochastic partial differential equations. (English) Zbl 1223.60044 J. Math. Anal. Appl. 384, No. 1, 70-86 (2011). MSC: 60H15 × Cite Format Result Cite Review PDF Full Text: DOI
Papavasiliou, A.; Pavliotis, G. A.; Stuart, A. M. Maximum likelihood drift estimation for multiscale diffusions. (English) Zbl 1171.62047 Stochastic Processes Appl. 119, No. 10, 3173-3210 (2009). MSC: 62M05 62F12 60H10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Pavliotis, G. A.; Stuart, A. M. Parameter estimation for multiscale diffusions. (English) Zbl 1137.82016 J. Stat. Phys. 127, No. 4, 741-781 (2007). Reviewer: Maria Christina Mariani (Las Cruces) MSC: 82C31 65C30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv