Asymptotic properties for the parameter estimation in stochastic (functional) differential equations with Hölder drift

References

• C. Amorino, A. Heidari, V. Pilipauskaitė, and M. Podolskij, Parameter estimation of discretely observed interacting particle systems, Stochastic Process. Appl. 163 (2023), pp. 350–386.
   Web of Science ®Google Scholar
• J. Bao and X. Huang, Approximations of McKean-Vlasov stochastic differential equations with irregular coefficients, J. Theor. Probab. 35 (2021), pp. 1187–1215.
   Web of Science ®Google Scholar
• J. Bao, X. Huang, and C. Yuan, Convergence rate of Euler-Maruyama scheme for SDEs with Hölder-Dini continuous drifts, J. Theor. Probab 32 (2019), pp. 848–871.
   Web of Science ®Google Scholar
• J. Bao and J. Shao, Weak convergence of path-dependent SDEs with irregular coefficients, preprint (2018). Available at arXiv:1809.03088.
   Google Scholar
• S. Biswas, C. Kumar, G.D. Reis, and C. Reisinger, Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by Lévy noise, preprint (2020). Available at arXiv:2010.08585.
   Google Scholar
• M. Delattre, V. Genon-Catalot, and C. Larédo, Parametric inference for discrete observations of diffusion processes with mixed effects, Stochastic Process. Appl. 128 (2018), pp. 1929–1957.
   Web of Science ®Google Scholar
• D. Florens-Zmirou, Approximate discrete-time schemes for statistics of diffusion processes, Statistics 20 (1989), pp. 547–557.
   Google Scholar
• A. Friedman, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, New York, 1975.
   Google Scholar
• I. Gyongy and T. Martinez, On stochastic differential equations with locally unbounded drift, Czechoslovak Math. J. 51 (2001), pp. 763–783.
   Web of Science ®Google Scholar
• X. Huang, Exponential convergence for functional SDEs with Hölder continuous drift, Stoch. Anal. Appl. 37 (2019), pp. 977–990.
   Web of Science ®Google Scholar
• X. Huang and F. Yang, Distribution-dependent SDEs with Hölder continuous drift and α-stable noise, Numer. Algor. 86 (2021), pp. 813–831.
   Web of Science ®Google Scholar
• X. Huang and S.Q. Zhang, Mild solutions and Harnack inequality for functional stochastic partial differential equations with Dini drift, J. Theor. Probab. 32 (2019), pp. 303–329.
   Web of Science ®Google Scholar
• M. Kessler, Estimation of an ergodic diffusion from discrete observations, Scand. J. Statist. 24 (1997), pp. 211–229.
   Web of Science ®Google Scholar
• N. Krylov and M. Röckner, Strong solutions of stochastic equations with singular time dependent drift, Probab. Theory Relat. Fields 131 (2005), pp. 154–196.
   Web of Science ®Google Scholar
• H. Long, Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises, Statist. Probab. Lett. 79 (2009), pp. 2076–2085.
   Web of Science ®Google Scholar
• H. Long, C. Ma, and Y. Shimizu, Least squares estimators for stochastic differential equations driven by small Lévy noises, Stoch. Proc. Appl. 127 (2017), pp. 1475–1495.
   Web of Science ®Google Scholar
• H. Long, Y. Shimizu, and W. Sun, Least squares estimators for discretely observed stochastic processes driven by small Lévy noises, J. Multivariate Anal. 116 (2013), pp. 422–439.
   Web of Science ®Google Scholar
• P. Ren and J.L. Wu, Least squares estimator for path-dependent McKean-Vlasov SDEs via disctete-time observations, Acta Math. Sci. Ser. B Engl. Ed 3 (2019), pp. 691–716.
   Google Scholar
• P. Ren and J.L. Wu, Least squares estimation for path-distribution dependent stochastic differential equations, Appl. Math. Comput. 410 (2021), p. 126457.
   Web of Science ®Google Scholar
• A. van der Vaart, Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, 1998.
   Google Scholar
• F.Y. Wang, Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift, J. Differ. Equations 260 (2016), pp. 2792–2829.
   Web of Science ®Google Scholar
• C. Wei and H. Shu, Maximum likelihood estimation for the drift parameter in diffusion processes, Stochastics 88 (2016), pp. 699–710.
   Web of Science ®Google Scholar
• J. Wen, X. Wang, S. Mao, and X. Xiao, Maximum likelihood estimation of McKean-Vlasov stochastic differential equation and its application, Appl. Math. Comput. 274 (2016), pp. 237–246.
   Web of Science ®Google Scholar
• N. Yoshida, Estimation for diffusion processes from discrete observation, J. Multivariate Anal. 41 (1992), pp. 220–242.
   Web of Science ®Google Scholar
• X. Zhang, Strong solutions of SDEs with singular drift and sobolev diffusion coefficients, Stochastic Process. Appl. 115 (2005), pp. 1805–1818.
   Web of Science ®Google Scholar
• X. Zhang, Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients, Electron. J. Probab. 16 (2011), pp. 1096–1116.
   Web of Science ®Google Scholar
• X. Zhang, Stochastic differential equations with Sobolev diffusion and singular drift and applications, Ann. Appl. Probab. 26 (2016), pp. 2697–2732.
   Web of Science ®Google Scholar