Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered.It is assumed that therandom variables {ζn } , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0.
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Key Findings & Data:In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered.It is assumed that therandom variables {ζn } , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0.
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Conclusion & Impact:Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Semi-Markovian random walk · a discrete interference of chance · Weibulldistribution
Abstract
In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered.It is assumed that therandom variables {ζn } , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0. Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.
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