Drift estimation for discretely sampled SPDEs

Bishwal, J.P.N.: Parameter Estimation in Stochastic Differential Equations. Lecture Notes in Mathematics, vol. 1923. Springer, Berlin (2008)

Bibinger, M., Trabs, M.: On central limit theorems for power variations of the solution to the stochastic heat equation. In: Proceedings in Mathematics and Statistics. Springer (Forthcoming) (2019)

Bibinger, M., Trabs, M.: Volatility estimation for stochastic PDEs using high-frequency observations. In: Stochastic Processes and their Applications (2019). https://doi.org/10.1016/j.spa.2019.09.002

Cheng, Z., Cialenco, I., Gong, R.: Bayesian estimations for diagonalizable bilinear SPDEs. In: Stochastic Processes and their Applications. (Forthcoming) (2019). https://doi.org/10.1016/j.spa.2019.03.020

Cialenco, I., Glatt-Holtz, N.: Parameter estimation for the stochastically perturbed Navier–Stokes equations. Stoch. Process. Appl. 121(4), 701–724 (2011)

Cialenco, I., Gong, R., Huang, Y.: Trajectory fitting estimators for SPDEs driven by additive noise. Stat. Inference Stoch. Process. 21(1), 1–19 (2018)

Cialenco, I., Huang, Y.: A note on parameter estimation for discretely sampled SPDEs. In: Stochastics and Dynamics (2019). https://doi.org/10.1142/S0219493720500161

Chow, P.: Stochastic Partial Differential Equations. Applied Mathematics and Nonlinear Science Series. Chapman & Hall, Boca Raton (2007)

Chong, C.: High-frequency analysis of parabolic stochastic PDEs. arXiv:1806.06959 (2019)

Cialenco, I.: Statistical inference for SPDEs: an overview. Stat. Inference Stoch. Process. 21(2), 309–329 (2018)

Cialenco, I., Lototsky, S.V., Pospíšil, J.: Asymptotic properties of the maximum likelihood estimator for stochastic parabolic equations with additive fractional Brownian motion. Stoch. Dyn. 9(2), 169–185 (2009)

Cialenco, I., Xu, L.: Hypothesis testing for stochastic PDEs driven by additive noise. Stoch. Process. Appl. 125(3), 819–866 (2015)

Lototsky, S.V.: Statistical inference for stochastic parabolic equations: a spectral approach. Publ. Mat. 53(1), 3–45 (2009)

Lototsky, S.V., Rozovsky, B.L.: Stochastic Partial Differential Equations. Springer, New York (2017)

Lototsky, S.V., Rozovsky, B.L.: Stochastic Evolution Systems. Linear Theory and Applications to Non-linear Filtering. Probability Theory and Stochastic Modelling, vol. 89, 2nd edn. Springer, New York (2018)

Markussen, B.: Likelihood inference for a discretely observed stochastic partial differential equation. Bernoulli 9(5), 745–762 (2003)

Nourdin, I., Peccati, G.: Normal Approximations with Malliavin Calculus, from Stein’s Method to Universality. Cambridge Tracts in Mathematics, vol. 192. Cambridge University Press, Cambridge (2012)

Nualart, D.: The Malliavin Calculus and Related Topics, Probability and Its Applications (New York), 2nd edn. Springer, Berlin (2006)

Piterbarg, L.I., Rozovskii, B.L.: On asymptotic problems of parameter estimation in stochastic PDE’s: discrete time sampling. Math. Methods Stat. 6(2), 200–223 (1997)

Prakasa Rao, B.L.S.: Nonparametric inference for a class of stochastic partial differential equations based on discrete observations. Sankhyā Ser. A 64(1), 1–15 (2002)

Prakasa Rao, B.L.S.: Estimation for some stochastic partial differential equations based on discrete observations. II. Calcutta Stat. Assoc. Bull. 54(215–216), 129–141 (2003)

Pasemann, G., Stannat, W.: Drift estimation for stochastic reaction–diffusion systems. Preprint arXiv:1904.04774v1 (2019)

Pospíšil, J., Tribe, R.: Parameter estimates and exact variations for stochastic heat equations driven by space-time white noise. Stoch. Anal. Appl. 25(3), 593–611 (2007)

Shiryaev, A.N.: Probability. Graduate Texts in Mathematics, vol. 2, 2nd edn. Springer, New York (1996)

Shubin, M.A.: Pseudodifferential Operators and Spectral Theory, 2nd edn. Springer, Berlin (2001)