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On Limit Theorems for Stationary Processes
Theory of Probability & Its Applications, 1962We give some new conditions for asymptotic normality of the time averages of stationary process. The methods of this paper were used earlier (see [3], 2) for proving the central limit. theorem for time means of functions given on the phase space of some classical dynamical systems.
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On Maxentropic Discrete Stationary Processes
Bell System Technical Journal, 1972This paper is concerned with the following mathematical problem. Let X denote a stationary time-discrete random process whose variables, …, X −1 , X 0 , X 1 , …, take values from the finite set of real numbers {x 1 , x 2 , …, x k }. Let X have mean zero and a given covariance sequence p k = EX i X i+k , j, k = 0, ±1, ±2, …. What is the largest entropy
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On the Problem of Filtration of Stationary Processes
Theory of Probability & Its Applications, 1962Let $x(t) = \int_{ - \infty }^\infty {e^{it\lambda } } dZ(\lambda )$ be a stationary process whose spectral density $f(\lambda ) = {|{B(\lambda )}|^2 } /{|{A(\lambda )}|^2} ;B(\lambda ), A(\lambda )$ are two polynomials. We study the properties of the spaces $H^{\Delta r} (t)$, where the $\Delta r(t)$ are the Fourier transforms of ${\Delta z(\lambda )}/
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Stationary Processes for Translation Operators
Proceedings of the London Mathematical Society, 1996We consider the class of Gaussian processes on complete manifolds of bounded curvature which are stationary under the generalized translation operation generated by the Laplace-Beltrami operator. We give a sufficient condition on the spectral density for the sample paths to be almost surely continuous.
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A Stochastic Harmonic Function Representation for Non-Stationary Stochastic Processes
Mechanical Systems and Signal Processing, 2017Fan Kong, Jianbing Chen, Yongbo Peng
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