Discounted payments theorems for large deviations
Aurelija Kasparavičiūtė
Vilnius Gediminas Technical University
Dovilė Deltuvienė
Vilnius Gediminas Technical University
Published 2016-12-15


cumulant method
large deviations
nonuniform estimate
the sum of discounted payments

How to Cite

Kasparavičiūtė A. and Deltuvienė D. (2016) “Discounted payments theorems for large deviations”, Lietuvos matematikos rinkinys, 57(A), pp. 29–34. doi: 10.15388/LMR.A.2016.06.



Let Z(t) = Σj=1N(t)Xj, t ≥ 0, be a stochastic process, where Xj are independent identically distributed random variables, and N(t) is non-negative integer-valued process with independent increments. Throughout, we assume that N(t) and Xj are independent. The paper considers normal approximation to the distribution of properly centered and normed random variable Zδ =∫0e- δtdZ(t), δ > 0, taking into consideration large deviations both in the Cramér zone and the power Linnik zones. Also, we obtain a nonuniform estimate in the Berry–Essen inequality. 

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