Kybernetika 56 no. 3, 410-431, 2020

Estimating the conditional expectations for continuous time stationary processes

Gusztáv Morvai and Benjamin WeissDOI: 10.14736/kyb-2020-3-0410


One of the basic estimation problems for continuous time stationary processes $X_t$, is that of estimating $E\{X_{t+\beta}| X_s : s \in [0, t]\}$ based on the observation of the single block $\{X_s : s \in [0, t]\}$ when the actual distribution of the process is not known. We will give fairly optimal universal estimates of this type that correspond to the optimal results in the case of discrete time processes.


nonparametric estimation, continuous time stationary processes


60G10, 60G25, 62G05


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