Precise asymptotics in Spitzer and Baum–Katz's law of large numbers: the semistable case
Copyright policy )Precise asymptotics in Spitzer and Baum–Katz's law of large numbers: the semistable case
Let \(X_1, X_2,\dots\) be i.i.d. random variables with \(EX=0\), and set \(S_{n}=X_1+\dots+X_{n}\). The paper contains the following results. Theorem 1. Assume that \(X_1\) belongs to the domain of semistable attraction of a nondegenerate semistable distribution with exponent \(\alpha\). If \(0
- TU Dortmund University Germany
Sums of independent random variables; random walks, tail probability of sums of independent identically distributed random variables, Applied Mathematics, Spitzer law, Infinitely divisible distributions; stable distributions, Tail probabilities of sums of i.i.d. random variables, Semistable distributions, Spitzer's law, semistable distribution, Baum–Katz's law, Baum-Katz law, Analysis
Sums of independent random variables; random walks, tail probability of sums of independent identically distributed random variables, Applied Mathematics, Spitzer law, Infinitely divisible distributions; stable distributions, Tail probabilities of sums of i.i.d. random variables, Semistable distributions, Spitzer's law, semistable distribution, Baum–Katz's law, Baum-Katz law, Analysis
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