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