On the Complete Convergence of Moving Average Process with Banach Space Valued Random Elements

2007 ◽  
Vol 21 (2) ◽  
pp. 431-436 ◽  
Author(s):  
Tae-Sung Kim ◽  
Mi-Hwa Ko
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Random Elements

A REMARK ON THE STRONG LAW FOR B-VALUED ARRAYS OF RANDOM ELEMENTS

2010 ◽  
Vol 82 (1) ◽  
pp. 31-43 ◽  
Author(s):  
TIEN-CHUNG HU ◽  
PING YAN CHEN ◽  
N. C. WEBER
Keyword(s):  
Law Of Large Numbers ◽  
Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Strong Law ◽  
Rate Law ◽  
Large Numbers ◽  
Random Elements

AbstractThe conditions in the strong law of large numbers given by Li et al. [‘A strong law for B-valued arrays’, Proc. Amer. Math. Soc.123 (1995), 3205–3212] for B-valued arrays are relaxed. Further, the compact logarithm rate law and the bounded logarithm rate law are discussed for the moving average process based on an array of random elements.

scholarly journals Complete Convergence for Moving Average Process of Martingale Differences

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wenzhi Yang ◽  
Shuhe Hu ◽  
Xuejun Wang
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Average Process ◽  
Moving Average Process ◽  
Martingale Differences ◽  
Moment Convergence ◽  
Moving Process

Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones.

scholarly journals On Complete Convergence of Moving Average Process for AANA Sequence

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Wenzhi Yang ◽  
Xuejun Wang ◽  
Nengxiang Ling ◽  
Shuhe Hu
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Partial Sums ◽  
Complete Moment Convergence ◽  
Average Process ◽  
Moving Average Process ◽  
Moment Convergence ◽  
The Moment ◽  
Asymptotically Almost Negatively Associated

We investigate the moving average process such thatXn=∑i=1∞aiYi+n,n≥1, where∑i=1∞|ai|<∞and{Yi,1≤i<∞}is a sequence of asymptotically almost negatively associated (AANA) random variables. The complete convergence, complete moment convergence, and the existence of the moment of supermum of normed partial sums are presented for this moving average process.

A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES

2020 ◽  
pp. 1-22
Author(s):  
Luis E. Nieto-Barajas ◽  
Rodrigo S. Targino
Keyword(s):  
Latent Variables ◽  
Moving Average ◽  
Real Data ◽  
Model Parameters ◽  
Average Process ◽  
Moving Average Process ◽  
Data Set ◽  
Run Off ◽  
Average Form ◽  
Reserve Estimates

ABSTRACT We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements

2002 ◽  
Vol 47 (3) ◽  
pp. 533-547 ◽  
Author(s):  
Tien-Chung Hu ◽  
Tien-Chung Hu ◽  
Deli Li ◽  
Deli Li ◽  
Andrew Rosalsky ◽  
...  
Keyword(s):  
Banach Space ◽  
Complete Convergence ◽  
Weighted Sums ◽  
Random Elements

scholarly journals Wavelet analysis for modeling suspended sediment discharge

2004 ◽  
Vol 35 (2) ◽  
pp. 165-174 ◽  
Author(s):  
Hafzullah Aksoy ◽  
Tanju Akar ◽  
N. Erdem Ünal
Keyword(s):  
Suspended Sediment ◽  
Moving Average ◽  
Haar Wavelet ◽  
Finite Variance ◽  
Sediment Discharge ◽  
Average Process ◽  
Moving Average Process ◽  
Discharge Time ◽  
Data Set ◽  
Environmental Processes

Wavelets, functions with zero mean and finite variance, have recently been found to be appropriate tools in investigating geophysical, hydrological, meteorological, and environmental processes. In this study, a wavelet-based modeling technique is presented for suspended sediment discharge time series. The model generates synthetic series statistically similar to the observed data. In the model in which the Haar wavelet is used, the available data are decomposed into detail functions. By choosing randomly from among the detail functions, synthetic suspended sediment discharge series are composed. Results are compared with those obtained from a moving-average process fitted to the data set.

Moving average process underlying the holographic–optical–tweezers experiments

2014 ◽  
Vol 53 (10) ◽  
pp. B254 ◽  
Author(s):  
Jakub Ślęzak ◽  
Sławomir Drobczyński ◽  
Karina Weron ◽  
Jan Masajada
Keyword(s):  
Optical Tweezers ◽  
Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Holographic Optical Tweezers
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