The stationarity of generalized STAR(2;λ1,λ2) process through the invers of autocovariance matrix

2014 ◽  
Author(s):  
Utriweni Mukhaiyar ◽  
Udjianna S. Pasaribu ◽  
Wono Setya Budhi ◽  
Khreshna Syuhada
Keyword(s):  
Autocovariance Matrix

Analysis of the Nonstationary Response of Vehicles With Multiple Wheels

1986 ◽  
Vol 108 (1) ◽  
pp. 69-73 ◽  
Author(s):  
R. F. Harrison ◽  
J. K. Hammond
Keyword(s):  
Random Processes ◽  
Time Variable ◽  
Variable Delay ◽  
Excitation Process ◽  
Nonstationary Random Process ◽  
Nonstationary Response ◽  
The Mean ◽  
Autocovariance Matrix ◽  
Ground Profile ◽  
Mean Vector

Vehicles moving on rough surfaces are subject to inputs which are often conveniently regarded as random processes. In general, the excitation process is “perceived” by the vehicle as a nonstationary random process either due to inhomogeneity in the ground profile or variations in the vehicle’s velocity, or both, Hitherto this second case has not been tractable analytically due to the time variable delay between inputs. In this paper this difficulty is overcome and expressions are derived for the propagation of the mean vector and zero-lag autocovariance matrix. An example of a vehicle modelled by a bicycle configuration is discussed.

scholarly journals The Structure of Autocovariance Matrix of Discrete Time Subfractional Brownian Motion

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Guo Jiang
Keyword(s):  
Brownian Motion ◽  
Discrete Time ◽  
Approximation Theorem ◽  
Finite Impulse Response ◽  
Structure Theorem ◽  
Stationary Processes ◽  
Time Varying ◽  
Subfractional Brownian Motion ◽  
Autocovariance Matrix ◽  
Impulse Response Filter

This article explores the structure of autocovariance matrix of discrete time subfractional Brownian motion and obtains an approximation theorem and a structure theorem to the autocovariance matrix of this stochastic process. Moreover, we give an expression to the unique time varying eigenvalue of the autocovariance matrix in asymptotic means and prove that the increments of subfractional Brownian motion are asymptotic stationary processes. At last, we illustrate these results with numerical experiments and give some probable applications in finite impulse response filter.

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