Tamed Euler–Maruyama approximation of McKean–Vlasov stochastic differential equations with super-linear drift and Hölder diffusion coefficients

Applied Numerical Mathematics - Tập 183 - Trang 56-85 - 2023
Huagui Liu1, Banban Shi1, Fuke Wu1
1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China

Tài liệu tham khảo

Antonelli, 2002, Rate of convergence of a particle method to the solution of the McKean-Vlasov equation, Ann. Appl. Probab., 12, 423, 10.1214/aoap/1026915611 Bao, 2022, Approximations of McKean-Vlasov stochastic differential equations with irregular coefficients, J. Theor. Probab., 35, 1187, 10.1007/s10959-021-01082-9 Bao, 2021, First-order convergence of Milstein schemes for McKean-Vlasov equations and interacting particle systems, Proc. R. Soc. A, 477, 10.1098/rspa.2020.0258 Bensoussan, 2013, Mean Field Games and Mean Field Type Control Theory, 10.1007/978-1-4614-8508-7 Budhiraja, 2017, Uniform in time interacting particle approximations for nonlinear equations of Patlak-Keller-Segel type, Electron. J. Probab., 22, 10.1214/17-EJP25 Carmona, 2018, Probabilistic Theory of Mean Field Games with Applications. I, vol. 83 Chaudru de Raynal, 2020, Strong well posedness of McKean-Vlasov stochastic differential equations with Hölder drift, Stoch. Process. Appl., 130, 79, 10.1016/j.spa.2019.01.006 Dawson, 1983, Critical dynamics and fluctuations for a mean-field model of cooperative behavior, J. Stat. Phys., 31, 29, 10.1007/BF01010922 dos Reis, 2022, Simulation of McKean-Vlasov SDEs with super-linear growth, IMA J. Numer. Anal., 42, 874, 10.1093/imanum/draa099 dos Reis, 2019, Freidlin-Wentzell LDP in path space for McKean-Vlasov equations and the functional iterated logarithm law, Ann. Appl. Probab., 29, 1487, 10.1214/18-AAP1416 Gobet, 2018, Analytical approximations of non-linear SDEs of McKean-Vlasov type, J. Math. Anal. Appl., 466, 71, 10.1016/j.jmaa.2018.05.059 Gyöngy, 2011, A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients, Stoch. Process. Appl., 121, 2189, 10.1016/j.spa.2011.06.008 Hammersley, 2021, McKean-Vlasov SDEs under measure dependent Lyapunov conditions, Ann. Inst. Henri Poincaré Probab. Stat., 57, 1032, 10.1214/20-AIHP1106 Higham, 2001, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43, 525, 10.1137/S0036144500378302 Higham, 2002, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM J. Numer. Anal., 40, 1041, 10.1137/S0036142901389530 Huang, 2021, Distribution dependent stochastic differential equations, Front. Math. China, 16, 257, 10.1007/s11464-021-0920-y Huang Huang, 2019, Distribution dependent SDEs with singular coefficients, Stoch. Process. Appl., 129, 4747, 10.1016/j.spa.2018.12.012 Huang, 2021, McKean-Vlasov SDEs with drifts discontinuous under Wasserstein distance, Discrete Contin. Dyn. Syst., 41, 1667, 10.3934/dcds.2020336 Hutzenthaler, 2011, Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 467, 1563 Hutzenthaler, 2012, Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients, Ann. Appl. Probab., 22, 1611, 10.1214/11-AAP803 Kloeden, 2010, Stochastic differential equations with nonlocal sample dependence, Stoch. Anal. Appl., 28, 937, 10.1080/07362994.2010.515194 Kloeden, 1992, Numerical Solution of Stochastic Differential Equations, vol. 23 Li, 2022, Strong convergence of Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations under local Lipschitz conditions of state variables, IMA J. Numer. Anal. Lions Mao, 2006 McKean, 1966, A class of Markov processes associated with nonlinear parabolic equations, Proc. Natl. Acad. Sci. USA, 56, 1907, 10.1073/pnas.56.6.1907 Milstein, 1995, Numerical Integration of Stochastic Differential Equations, vol. 313 Ngo, 2017, Strong rate of tamed Euler-Maruyama approximation for stochastic differential equations with Hölder continuous diffusion coefficient, Braz. J. Probab. Stat., 31, 24, 10.1214/15-BJPS301 Röckner, 2021, Well-posedness of distribution dependent SDEs with singular drifts, Bernoulli, 27, 1131, 10.3150/20-BEJ1268 Shiryaev, 1996, Probability, vol. 95 Stroock, 2006, Multidimensional Diffusion Processes Sznitman, 1991, Topics in propagation of chaos, vol. 1464, 165 Wang, 2018, Distribution dependent SDEs for Landau type equations, Stoch. Process. Appl., 128, 595, 10.1016/j.spa.2017.05.006 Yamada, 1971, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ., 11, 155 Yan, 2002, The Euler scheme with irregular coefficients, Ann. Probab., 30, 1172, 10.1214/aop/1029867124 Yang, 2020, The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients, J. Comput. Appl. Math., 366, 10.1016/j.cam.2019.112379 Yuan, 2008, A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations, Stoch. Anal. Appl., 26, 325, 10.1080/07362990701857251 Zhang, 2019, A discretized version of Krylov's estimate and its applications, Electron. J. Probab., 24, 10.1214/19-EJP390