Asymptotic behavior of the spectrum of a convolution operator on a finite interval with the transform of the integral kernel being a characteristic function

2010 ◽  
Vol 46 (10) ◽  
pp. 1519-1523 ◽  
Author(s):  
A. A. Polosin
Keyword(s):  
Asymptotic Behavior ◽  
Characteristic Function ◽  
Convolution Operator ◽  
Finite Interval ◽  
Integral Kernel

THE ASYMPTOTIC BEHAVIOR OF SEMI-INVARIANTS FOR LINEAR STOCHASTIC SYSTEMS

2002 ◽  
Vol 02 (02) ◽  
pp. 281-294
Author(s):  
G. N. MILSTEIN
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Exponent ◽  
Linear System ◽  
Characteristic Function ◽  
Stochastic Systems ◽  
Random Variable ◽  
Characteristic Functions ◽  
Linear Stochastic Systems ◽  
Moment Lyapunov Exponent ◽  
The Moment

The asymptotic behavior of semi-invariants of the random variable ln |X(t,x)|, where X(t,x) is a solution of a linear system of stochastic differential equations, is connected with the moment Lyapunov exponent g(p). Namely, it is obtained that the nth semi-invariant is asymptotically proportional to the time t with the coefficient of proportionality g(n)(0). The proof is based on the concept of analytic characteristic functions. It is also shown that the asymptotic behavior of the analytic characteristic function of ln |X(t,x)| in a neighborhood of the origin of the complex plane is controlled by the extension g(iz) of g(p).

A new approach to the convolution operator on a finite interval

1996 ◽  
Vol 26 (4) ◽  
pp. 460-475 ◽  
Author(s):  
P. A. Lopes ◽  
A. F. dos Santos
Keyword(s):  
Convolution Operator ◽  
Finite Interval ◽  
New Approach

Asymptotic behavior of characteristic function of simple serial rank statistics

2017 ◽  
Vol 11 ◽  
pp. 1307-1312
Author(s):  
Chikhi El Mokhtar ◽  
Hammou El Hachmi ◽  
Rifi Khalid
Keyword(s):  
Asymptotic Behavior ◽  
Characteristic Function ◽  
Rank Statistics

The Fredholm Approach to Asymptotic Inference on Nonstationary and Noninvertible Time Series Models

1990 ◽  
Vol 6 (4) ◽  
pp. 411-432 ◽  
Author(s):  
Katsuto Tanaka
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Characteristic Function ◽  
Limit Theorems ◽  
Fredholm Determinant ◽  
Linear Process ◽  
Time Series Models ◽  
Test Statistics ◽  
Unified Approach ◽  
Linear Forms

A unified approach which I call the Fredholm approach is suggested for the study of asymptotic behavior of estimators and" test statistics arising from nonstationary and/or noninvertible time series models. Some limit theorems are given concerning the distribution of (the ratio of) quadratic (plus linear) forms in random variables generated by a linear process that is not necessarily stationary. Especially, the limiting characteristic function is derived explicitly via the Fredholm determinant and resolvent of a given kernel. Some examples are also shown to illustrate our methodology.

Sign in / Sign up

Export Citation Format

Share Document