Limit Theorems for Functionals of Sample Functions of a Stationary Gaussian Process

1967 ◽  
Vol 12 (2) ◽  
pp. 320-323
Author(s):  
Yu. M. Ryzhov
Keyword(s):  
Gaussian Process ◽  
Limit Theorems ◽  
Stationary Gaussian Process

Records in the presence of a linear trend

1987 ◽  
Vol 19 (04) ◽  
pp. 801-828 ◽  
Author(s):  
Rocco Ballerini ◽  
Sidney I. Resnick
Keyword(s):  
Gaussian Process ◽  
Limit Theorems ◽  
Linear Trend ◽  
Random Sequence ◽  
Record Values ◽  
Stationary Gaussian Process ◽  
Record Times

Records from the sequence Yn = Xn + cn, n ≧ 1 are analyzed, where {Xn } is a strictly stationary random sequence. We prove various limit theorems for the record rate, record times, and record values. The situation when {Xn } is a stationary Gaussian process is considered with special attention given to Gaussian ARMA sequences. Data for the 400 and 800 metre races are used to illustrate these results.

Records in the presence of a linear trend

1987 ◽  
Vol 19 (4) ◽  
pp. 801-828 ◽  
Author(s):  
Rocco Ballerini ◽  
Sidney I. Resnick
Keyword(s):  
Gaussian Process ◽  
Limit Theorems ◽  
Linear Trend ◽  
Random Sequence ◽  
Record Values ◽  
Stationary Gaussian Process ◽  
Record Times

Records from the sequence Yn = Xn + cn, n ≧ 1 are analyzed, where {Xn} is a strictly stationary random sequence. We prove various limit theorems for the record rate, record times, and record values. The situation when {Xn} is a stationary Gaussian process is considered with special attention given to Gaussian ARMA sequences. Data for the 400 and 800 metre races are used to illustrate these results.

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