scholarly journals A Note on the Dependence Conditions for Stationary Normal Sequences

2015 ◽  
Vol 22 (6) ◽  
pp. 647-653 ◽  
Author(s):  
Hyemi Choi
Keyword(s):  
Dependence Conditions

Joint exceedances of high levels under a local dependence condition

1993 ◽  
Vol 30 (01) ◽  
pp. 112-120
Author(s):  
Helena Ferreira
Keyword(s):  
Order Statistics ◽  
Long Range ◽  
Joint Distribution ◽  
Long Range Dependence ◽  
Local Dependence ◽  
Stationary Sequences ◽  
Compound Poisson ◽  
Dependence Conditions

Under appropriate long-range dependence conditions, it is well known that the joint distribution of the number of exceedances of several high levels is asymptotically compound Poisson. Here we investigate the structure of a cluster of exceedances for stationary sequences satisfying a suitable local dependence condition, under which it is only necessary to get certain limiting probabilities, easy to compute, in order to obtain limiting results for the highest order statistics, exceedance counts and upcrossing counts.

Optimal Stopping Under General Dependence Conditions

1983 ◽  
Vol 26 (3) ◽  
pp. 260-266
Author(s):  
M. Longnecker
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Random Variables ◽  
Stopping Times ◽  
Dependence Conditions ◽  
Series Type

AbstractLet {Xn} be a sequence of random variables, not necessarily independent or identically distributed, put and Mn =max0≤k≤n|Sk|. Effective bounds on in terms of assumed bounds on , are used to identify conditions under which an extended-valued stopping time τ exists. That is these inequalities are used to guarantee the existence of the stopping time τ such that E(ST/aτ) = supt ∈ T∞ E(|Sτ|/at), where T∞ denotes the class of randomized extended-valued stopping times based on S1, S2, … and {an} is a sequence of constants. Specific applications to stochastic processes of the time series type are considered.

scholarly journals Asymptotics of Maxima of Strongly Dependent Gaussian Processes

2012 ◽  
Vol 49 (04) ◽  
pp. 1106-1118 ◽  
Author(s):  
Zhongquan Tan ◽  
Enkelejd Hashorva ◽  
Zuoxiang Peng
Keyword(s):  
Correlation Function ◽  
Long Range ◽  
Gaussian Processes ◽  
Limit Distribution ◽  
Strong Dependence ◽  
Dependence Conditions ◽  
Stationary Gaussian Processes

Let {Xn(t),t∈[0,∞)},n∈ℕ, be standard stationary Gaussian processes. The limit distribution oft∈[0,T(n)]|Xn(t)| is established asrn(t), the correlation function of {Xn(t),t∈[0,∞)},n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

scholarly journals On exact strong laws of large numbers under general dependence conditions

2018 ◽  
Vol 38 (1) ◽  
pp. 103-121 ◽  
Author(s):  
André Adler ◽  
Przemysław Matuła
Keyword(s):  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Dependence Conditions

We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.

Rates of convergence in some SLLN under weak dependence conditions

2010 ◽  
Vol 76 (3-4) ◽  
pp. 683-695
Author(s):  
Paul Doukhan ◽  
Oleg Klesov ◽  
Gabriel Lang
Keyword(s):  
Rates Of Convergence ◽  
Weak Dependence ◽  
Dependence Conditions
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