Strong invariance principles for dependent random variables
Wei Biao Wu
TL;DR
This paper develops strong invariance principles for dependent stationary processes, providing nearly optimal bounds and applications to laws of large numbers and iterated logarithm, advancing understanding of dependent random variables.
Contribution
It introduces nearly optimal bounds for invariance principles in dependent processes and applies them to derive classical probabilistic laws.
Findings
Established strong invariance principles with optimal bounds for dependent processes.
Derived strong laws of large numbers and laws of the iterated logarithm under verifiable conditions.
Applied results to linear and nonlinear stationary processes.
Abstract
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.
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