Abstract: Let Xi be a Lacunary System, we established large
deviations inequality for Lacunary System. Furthermore, we gained
Marcinkiewicz Larger Number Law with dependent random variables
sequences.
Abstract: Strong law of large numbers and complete convergence for sequences of *-mixing random variables are investigated. In particular, Teicher-s strong law of large numbers for independent random variables are generalized to the case of *-mixing random sequences and extended to independent and identically distributed Marcinkiewicz Law of large numbers for *-mixing.
Abstract: In this paper we consider a one-dimensional random
geometric graph process with the inter-nodal gaps evolving according
to an exponential AR(1) process. The transition probability matrix
and stationary distribution are derived for the Markov chains concerning
connectivity and the number of components. We analyze the
algorithm for hitting time regarding disconnectivity. In addition to
dynamical properties, we also study topological properties for static
snapshots. We obtain the degree distributions as well as asymptotic
precise bounds and strong law of large numbers for connectivity
threshold distance and the largest nearest neighbor distance amongst
others. Both exact results and limit theorems are provided in this
paper.
Abstract: In This Article We establish moment inequality of
dependent random variables,furthermore some theorems of strong law
of large numbers and complete convergence for sequences of dependent
random variables. In particular, independent and identically
distributed Marcinkiewicz Law of large numbers are generalized to
the case of m0-dependent sequences.