Our research focuses on parameter estimation for the stochastic fractional pseudo-parabolic equation (SFPPE), which is propelled by cylindrical Brownian motion. Within the spectral approach framework, we have formulated a maximum likelihood type (MLE-like) estimator for the drift parameter \(\theta \) . Subsequently, by segmenting the observation period [0, T] into M intervals, we have also developed a natural time discretization for this MLE-like estimator. We have conducted an analysis of the consistency and asymptotic normality of our estimators, considering a fixed time duration T, a large number of Fourier modes N, and a large number of time grid points M. The presence of a space-time mixed partial derivative term in the SFPPE reveals that the interplay between the orders of the differential operators and the spatial dimension d significantly influences the conditions for achieving consistency and asymptotic normality of the estimators. In contrast with the stochastic fractional heat equation (SFHE), the derived conditions for the SFPPE are fundamentally different. Additionally, the requirements for the time grid numbers M to ensure consistency and asymptotic normality for the discrete MLE-like estimator of the SFPPE are less stringent compared to those for the SFHE.
