On Conditions for the Applicability of the Strong Law of Large Numbers to Wide Sense Stationary Processes

1966 ◽  
Vol 11 (4) ◽  
pp. 632-636 ◽  
Author(s):  
I. N. Verbickaja
Keyword(s):  
Law Of Large Numbers ◽  
Stationary Processes ◽  
Wide Sense ◽  
Strong Law ◽  
Large Numbers

On rate conservation for non-stationary processes

1991 ◽  
Vol 28 (4) ◽  
pp. 762-770 ◽  
Author(s):  
Ravi Mazumdar ◽  
Raghavan Kannurpatti ◽  
Catherine Rosenberg
Keyword(s):  
Path Integration ◽  
Law Of Large Numbers ◽  
Direct Consequence ◽  
Time Dependent ◽  
Stationary Processes ◽  
Strong Law ◽  
Large Numbers ◽  
Stationary Version ◽  
Stationary Point Process ◽  
Cadlag Processes

This paper extends the rate conservation principle to cadlag processes whose jumps form a non-stationary point process with a time-dependent intensity. It is shown that this is a direct consequence of path integration and the strong law of large numbers for local martingales. When specialized to mean rates a non-stationary version of Miyazawa's result is obtained which is recovered in the stationary case. Some applications of the result are also given.

scholarly journals Limit theorems for locally stationary processes

2020 ◽  
Author(s):  
Rafael Kawka
Keyword(s):  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Moving Average ◽  
Stationary Processes ◽  
Time Varying ◽  
Strong Law ◽  
Large Numbers ◽  
Moving Average Representation ◽  
Locally Stationary Processes ◽  
Average Representation

Abstract We present limit theorems for locally stationary processes that have a one sided time-varying moving average representation. In particular, we prove a central limit theorem (CLT), a weak and a strong law of large numbers (WLLN, SLLN) and a law of the iterated logarithm (LIL) under mild assumptions using a time-varying Beveridge–Nelson decomposition.

On rate conservation for non-stationary processes

1991 ◽  
Vol 28 (04) ◽  
pp. 762-770 ◽  
Author(s):  
Ravi Mazumdar ◽  
Raghavan Kannurpatti ◽  
Catherine Rosenberg
Keyword(s):  
Path Integration ◽  
Law Of Large Numbers ◽  
Direct Consequence ◽  
Time Dependent ◽  
Stationary Processes ◽  
Strong Law ◽  
Large Numbers ◽  
Stationary Version ◽  
Stationary Point Process ◽  
Cadlag Processes

This paper extends the rate conservation principle to cadlag processes whose jumps form a non-stationary point process with a time-dependent intensity. It is shown that this is a direct consequence of path integration and the strong law of large numbers for local martingales. When specialized to mean rates a non-stationary version of Miyazawa's result is obtained which is recovered in the stationary case. Some applications of the result are also given.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

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