Limit Theorems for Functionals of Higher Order Differences of Brownian Semi-Stationary Processes

2012 ◽  
pp. 69-96 ◽  
Author(s):  
Ole E. Barndorff-Nielsen ◽  
José Manuel Corcuera ◽  
Mark Podolskij
Keyword(s):  
Limit Theorems ◽  
Higher Order ◽  
Stationary Processes

Limit theorems for maxima and crossings of a sequence of Gaussian processes and approximation of random processes

1991 ◽  
Vol 28 (01) ◽  
pp. 17-32 ◽  
Author(s):  
O. V. Seleznjev
Keyword(s):  
Gaussian Processes ◽  
Limit Distribution ◽  
Limit Theorems ◽  
Point Processes ◽  
Random Processes ◽  
Trigonometric Polynomials ◽  
Stationary Processes ◽  
Periodic Processes

We consider the limit distribution of maxima and point processes, connected with crossings of an increasing level, for a sequence of Gaussian stationary processes. As an application we investigate the limit distribution of the error of approximation of Gaussian stationary periodic processes by random trigonometric polynomials in the uniform metric.

Limit theorems for maxima and crossings of a sequence of Gaussian processes and approximation of random processes

1991 ◽  
Vol 28 (1) ◽  
pp. 17-32 ◽  
Author(s):  
O. V. Seleznjev
Keyword(s):  
Gaussian Processes ◽  
Limit Distribution ◽  
Limit Theorems ◽  
Point Processes ◽  
Random Processes ◽  
Trigonometric Polynomials ◽  
Stationary Processes ◽  
Periodic Processes

We consider the limit distribution of maxima and point processes, connected with crossings of an increasing level, for a sequence of Gaussian stationary processes. As an application we investigate the limit distribution of the error of approximation of Gaussian stationary periodic processes by random trigonometric polynomials in the uniform metric.

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (4) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (04) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

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