On a limit theorem for a stochastic process related to quantum biophysics of vision

1963 ◽  
Vol 15 (1) ◽  
pp. 167-175 ◽  
Author(s):  
Keiiti Isii
Keyword(s):  
Stochastic Process ◽  
Limit Theorem

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.

scholarly journals Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima

2017 ◽  
Vol 15 (1) ◽  
pp. 1024-1034 ◽  
Author(s):  
Marcin Dudziński ◽  
Konrad Furmańczyk
Keyword(s):  
Stochastic Process ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Archimedean Copula ◽  
Archimedean Copulas ◽  
Continuous Type ◽  
The Family

Abstract Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’s (X1, ...,Xn) has the Archimedean copula CΨ.

scholarly journals A central limit theorem for empirical processes

1982 ◽  
Vol 33 (2) ◽  
pp. 235-248 ◽  
Author(s):  
David Pollard
Keyword(s):  
Stochastic Process ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Empirical Processes ◽  
Empirical Measure ◽  
Integrable Functions ◽  
New Form ◽  
Square Integrable Functions ◽  
Functional Central Limit

AbstractThe empirical measure Pn for independent sampling on a distribution P is formed by placing mass n−1 at each of the first n sample points. In this paper, n½(Pn − P) is regarded as a stochastic process indexed by a family of square integrable functions. A functional central limit theorem is proved for this process. The statement of this theorem involves a new form of combinatorial entropy, definable for classes of square integrable functions.

scholarly journals A Limit Theorem for a Weiss Epidemic Process

2015 ◽  
Vol 52 (1) ◽  
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.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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