On approximations for the distribution of first level crossing time

2017/08/29 by V. K. Malinovskiǐ, Malinovskii, Vsevolod K., Konstantin V. Malinovskii +1 · 2 citations
Mathematics · #Mathematical Approximation and Integration #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1708.08678

Abstract

We investigate performance of approximations put forth in \citeNP[Malinovskii 2017a] and \citeNP[Malinovskii 2017b] for the distribution of the time of first level u crossing by the random process \homVs-cs, s>0, where \homVs is compound renewal process. In the case of Exponential inter-renewal and jump size random variables, we compare the approximations with exact and with simulation results. In a few other cases including Erlang and Pareto inter-renewal and jump size random variables, where exact results are absent, we compare the approximations with simulation results.

Cited by

• Approximation of the fixed-probability level for a compound renewal process
• On approximations for the distribution of the time of first level crossing

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