Limit theorems for sums of independent random variables defined on a nonrecurrent random walk
Copyright policy )Limit theorems for sums of independent random variables defined on a nonrecurrent random walk
Let {Xi}i=∞ -∞, {ξi}i=1∞ be two independent sequences of randoms variables, where the ξi are identically distributed and assume integer values. Let In the paper the question of the asymptotic behavior as n → ∞ of the quantity is considered. It is shown that the distribution of Wn converges to the distribution of the normal law and that the estimate of the rate of convergence has the same order as the classical estimate of Berry-Esseen.
Sums of independent random variables; random walks, integer lattice, asymptotic behaviour, limit theorems, Central limit and other weak theorems, recurrent random walk, Berry-Esseen estimate, random walk, sums of independent random variables, asymptotic behavior, Brownian local time
Sums of independent random variables; random walks, integer lattice, asymptotic behaviour, limit theorems, Central limit and other weak theorems, recurrent random walk, Berry-Esseen estimate, random walk, sums of independent random variables, asymptotic behavior, Brownian local time
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