A spectral limit theorem on a non-linear stochastic process with non-additive, independent, linear components

1977 ◽  
Vol 29 (1) ◽  
pp. 101-118 ◽  
Author(s):  
K. N. Venkataraman
Keyword(s):  
Stochastic Process ◽  
Limit Theorem ◽  
Non Linear

The Equivalent Gain Matrix of a Multivariable Non-Linearity

1969 ◽  
Vol 2 (1) ◽  
pp. T1-T5 ◽  
Author(s):  
John C. West
Keyword(s):  
Stochastic Process ◽  
Cross Correlation ◽  
Linear Matrix ◽  
Sinusoidal Wave ◽  
Gain Matrix ◽  
Cross Modulation ◽  
Input Signals ◽  
Non Linear ◽  
Wave Forms ◽  
Random Signals

The equivalent gain concept of a mono-variable non-linear stochastic process is used to evaluate the linear matrix equivalent of a multi-variable non-linearity having n independent inputs and m outputs. It is shown that if the n inputs are restricted to separable class of processes (which includes Gaussian random signals and also sinusoidal wave forms but is much wider), then the distortion terms produced by the non-linearity and by cross modulation have zero cross-correlation with any of the input signals.

The Testing Filtering and Majorized Algorithm of a Kind of Nonstationary Stochastic Transmission System in Intelligence Control

2014 ◽  
Vol 926-930 ◽  
pp. 3581-3584
Author(s):  
Xiao Nan Xiao
Keyword(s):  
Stochastic Process ◽  
Optimal Control ◽  
Mathematical Models ◽  
Incomplete Data ◽  
Transmission System ◽  
Linear Filtering ◽  
Optimal Coding ◽  
Non Linear ◽  
Intelligence Control ◽  
Nonstationary Stochastic Process

In intelligence control, applying the method of optimal non-linear filtering and majorized algorithm, this paper discusses the optimal control of a kind of incomplete data and continuous nonstationary stochastic process; yields two optimal control mathematical models in these two situations; illustrates how to establish the optimal coding and decoding of the nonstationary stochastic process; and provides an effective and reliable approach for the optimal control of such a process.

Product autoregression: a time-series characterization of the gamma distribution

1982 ◽  
Vol 19 (2) ◽  
pp. 463-468 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Gamma Distribution ◽  
Stationary Stochastic Process ◽  
Correlation Structure ◽  
First Order ◽  
Non Linear ◽  
Autoregressive Correlation

A non-linear stationary stochastic process {Xt} is derived and shown to have the property that both the processes {Xt} and {log Xt} have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discussed briefly and a characterization of the gamma distribution is obtained.

A Limit Theorem for a Weiss Epidemic Process

2015 ◽  
Vol 52 (01) ◽  
pp. 247-257 ◽  
Author(s):  
A. V. Kalinkin ◽  
A. V. Mastikhin
Keyword(s):  
Stochastic Process ◽  
Limit Theorem ◽  
Generating Function ◽  
Transition Probabilities ◽  
Special Functions ◽  
Death Process ◽  
Two Dimensional ◽  
Kolmogorov Equations ◽  
Fourier Methods ◽  
Double Generating Function

For a Markov two-dimensional death-process of a special class we consider the use of Fourier methods to obtain an exact solution of the Kolmogorov equations for the exponential (double) generating function of the transition probabilities. Using special functions, we obtain an integral representation for the generating function of the transition probabilities. We state the expression of the expectation and variance of the stochastic process and establish a limit theorem.

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