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Abstract
ABSTRACTA semi-Markovian random walk process (X(t)) with a generalized beta distribution of chance is considered. The asymptotic expansions for the first four moments of the ergodic distribution of the process are obtained as E(ζn) → ∞ when the random variable ζn has a generalized beta distribution with parameters (s, S, α, β); α, β > 1, 0 ⩽ s < S < ∞. Finally, the accuracy of the asymptotic expansions is examined by using the Monte Carlo simulation method.
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