Sharp Bounds for Exponential Approximations of NWUE Distributions
Let F be an NWUE distribution with mean 1 and G be the stationary renewal distribution of F. We would expect G to converge in distribution to the unit exponential distribution as its mean goes to 1. In this paper, we derive sharp bounds for the Kolmogorov distance between G and the unit exponential distribution, as well as between G and an exponential distribution with the same mean as G. We apply the bounds to geometric convolutions and to first passage times.
KeywordsSharp error bounds for exponential approximations One and two-sided Kolmogorov distances Equilibrium distributions Geometric convolutions First passage times in time reversible Markov chains NWUE distributions
Mathematics Subject Classification (2010)60E15 60J27 60K10 60K25 90B25
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