Wong–Zakai approximations and support theorems for stochastic McKean–Vlasov equations

References

[1] V. Bally, A. Millet and M. Sanz-Solé, Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations, Ann. Probab. 23 (1995), no. 1, 178–222. 10.1214/aop/1176988383Suche in Google Scholar

[2] J. Bao and X. Huang, Approximations of Mckean–Vlasov SDEs with irregular coefficients, preprint (2019), https://arxiv.org/abs/1905.08522. Suche in Google Scholar

[3] J. Bao, C. Reisinger, P. Ren and W. Stockinger, First-order convergence of Milstein schemes for McKean–Vlasov equations and interacting particle systems, Proc. A. 477 (2021), no. 2245, Paper No. 20200258. 10.1098/rspa.2020.0258Suche in Google Scholar PubMed PubMed Central

[4] J. Bao, C. Reisinger, P. Ren and W. Stockinger, Milstein schemes for delay Mckean equations and interacting particle systems, preprint (2020), https://arxiv.org/abs/2005.01165. Suche in Google Scholar

[5] J. Bao and J. Shao, Weak convergence of path-dependent SDEs with irregular coefficients, preprint (2018), https://arxiv.org/abs/1809.03088. Suche in Google Scholar

[6] Y. Cai, J. Huang and V. Maroulas, Large deviations of mean-field stochastic differential equations with jumps, Statist. Probab. Lett. 96 (2015), 1–9. 10.1016/j.spl.2014.08.010Suche in Google Scholar

[7] P. E. Chaudru de Raynal, Strong well posedness of McKean–Vlasov stochastic differential equations with Hölder drift, Stochastic Process. Appl. 130 (2020), no. 1, 79–107. 10.1016/j.spa.2019.01.006Suche in Google Scholar

[8] I. Chueshov and A. Millet, Stochastic two-dimensional hydrodynamical systems: Wong–Zakai approximation and support theorem, Stoch. Anal. Appl. 29 (2011), no. 4, 570–611. 10.1080/07362994.2011.581081Suche in Google Scholar

[9] D. Crisan and E. McMurray, Smoothing properties of McKean–Vlasov SDEs, Probab. Theory Related Fields 171 (2018), no. 1–2, 97–148. 10.1007/s00440-017-0774-0Suche in Google Scholar

[10] T. E. Govindan and N. U. Ahmed, On Yosida approximations of McKean–Vlasov type stochastic evolution equations, Stoch. Anal. Appl. 33 (2015), no. 3, 383–398. 10.1080/07362994.2014.993766Suche in Google Scholar

[11] I. Gyöngy and T. Pröhle, On the approximation of stochastic differential equation and on Stroock–Varadhan’s support theorem, Comput. Math. Appl. 19 (1990), no. 1, 65–70. 10.1016/0898-1221(90)90082-USuche in Google Scholar

[12] Y. Hu, A. Matoussi and T. Zhang, Wong–Zakai approximations of backward doubly stochastic differential equations, Stochastic Process. Appl. 125 (2015), no. 12, 4375–4404. 10.1016/j.spa.2015.07.003Suche in Google Scholar

[13] T. Ma and R. Zhu, Wong–Zakai approximation and support theorem for SPDEs with locally monotone coefficients, J. Math. Anal. Appl. 469 (2019), no. 2, 623–660. 10.1016/j.jmaa.2018.09.031Suche in Google Scholar

[14] V. Mackevic̆ius, The support of the solution of a stochastic differential equation, Lith. Math. J. 26 (1986), 57–62. 10.1007/BF00971347Suche in Google Scholar

[15] X. Mao, Stochastic Differential Equations and Applications, 2nd ed., Horwood, Chichester, 2007. 10.1533/9780857099402Suche in Google Scholar

[16] H. P. McKean, Jr., A class of Markov processes associated with nonlinear parabolic equations, Proc. Natl. Acad. Sci. USA 56 (1966), 1907–1911. 10.1073/pnas.56.6.1907Suche in Google Scholar PubMed PubMed Central

[17] H. P. McKean, Jr., Propagation of chaos for a class of non-linear parabolic equations, Stochastic Differential Equations, Air Force Office Sci. Res., Arlington (1967), 41–57. Suche in Google Scholar

[18] A. Millet and M. Sanz-Solé, A simple proof of the support theorem for diffusion processes, Séminaire de Probabilités 28, Lecture Notes in Math. 1583, Springer, Berlin (1994), 36–48. 10.1007/BFb0073832Suche in Google Scholar

[19] A. Millet and M. Sanz-Solé, Approximation and support theorem for a wave equation in two space dimensions, Bernoulli 6 (2000), no. 5, 887–915. 10.2307/3318761Suche in Google Scholar

[20] H. Qiao, Euler–Maruyama approximations for stochastic Mckean–Vlasov equations with non-Lipschitz coefficents, preprint (2019), https://arxiv.org/abs/1903.01175. Suche in Google Scholar

[21] J. Ren and J. Wu, On approximate continuity and the support of reflected stochastic differential equations, Ann. Probab. 44 (2016), no. 3, 2064–2116. 10.1214/15-AOP1018Suche in Google Scholar

[22] J. Ren and X. Zhang, Limit theorems for stochastic differential equations with discontinuous coefficients, SIAM J. Math. Anal. 43 (2011), no. 1, 302–321. 10.1137/10078952XSuche in Google Scholar

[23] D. W. Stroock and S. R. S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Vol. III: Probability Theory, University of California, Oakland (1972), 333–359. 10.1525/9780520375918-020Suche in Google Scholar

[24] E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist. 36 (1965), 1560–1564. 10.1214/aoms/1177699916Suche in Google Scholar

[25] J. Wu and M. Zhang, Limit theorems and the support of SDES with oblique reflections on nonsmooth domains, J. Math. Anal. Appl. 466 (2018), no. 1, 523–566. 10.1016/j.jmaa.2018.06.004Suche in Google Scholar

[26] T. Zhang, Strong convergence of Wong–Zakai approximations of reflected SDEs in a multidimensional general domain, Potential Anal. 41 (2014), no. 3, 783–815. 10.1007/s11118-014-9394-9Suche in Google Scholar