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Precise large deviations for strong subexponential distributions and applications on a multi risk model

Abstract We investigate the asymptotic relations for sums of independent identically distributed random variables when the distribution function belongs to the heavy tailed class. Also, we investigate if the asymptotic relation of large deviations holds, when the relation between x and n is linear, for all subexponential tailed distribution functions using the example of Weibull distribution. Finally, we apply the main result on the multi risk model it was introduced in Wang and Wang (2007).