scholarly journals The prediction theory of multivariate stochastic processes, III: Unbounded spectral densities

1960 ◽  
Vol 104 (1-2) ◽  
pp. 141-162 ◽  
Author(s):  
P. Masani
Keyword(s):  
Stochastic Processes ◽  
Spectral Densities ◽  
Prediction Theory

scholarly journals Non-Linear prediction problems for Ornstein-Uhlenbeck process

1983 ◽  
Vol 91 ◽  
pp. 173-184 ◽  
Author(s):  
Sheu-San Lee
Keyword(s):  
Stochastic Processes ◽  
Linear Functional ◽  
Linear Prediction ◽  
Basic Process ◽  
Prediction Theory ◽  
Uhlenbeck Process ◽  
Linear Predictor ◽  
Ornstein Uhlenbeck Process ◽  
Non Linear ◽  
Prediction Problems

We shall discuss in this paper some problems in non-linear prediction theory. An Ornstein-Uhlenbeck process {U(t)} is taken to be a basic process, and we shall deal with stochastic processes X(t) that are transformed by functions f satisfying certain condition. Actually, observed processes are expressed in the form X(t) = f(U(t)). Our main problem is to obtain the best non-linear predictor X̂(t, τ) for X(t + τ), τ > 0, assuming that X(s), s ≤t, are observed. The predictor is therefore a non-linear functional of the values X(s), s ≤ t.

scholarly journals Superoscillations and Analytic Extension in Schur Analysis

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Irene Sabadini
Keyword(s):  
Stochastic Processes ◽  
Positive Definite ◽  
Signal Theory ◽  
Positive Definite Functions ◽  
Analytic Extension ◽  
Prediction Theory ◽  
Stationary Stochastic Processes

AbstractWe give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of R-functions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

Prediction Theory of Periodically Correlated Stochastic Processes

2015 ◽  
Author(s):  
Abolghassem Miamee ◽  
Andrzej Makagon
Keyword(s):  
Stochastic Processes ◽  
Prediction Theory

Stochastic Processes in Demography and Applications

1992 ◽  
Vol 46 (1) ◽  
pp. 172-173
Author(s):  
S. Mitra
Keyword(s):  
Stochastic Processes
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