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Displaying similar documents to “Large deviations of sums of independent random variables”

An asymptotic expansion for the distribution of the supremum of a random walk

M. Sgibnev (2000)

Studia Mathematica

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Let S n be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of S n which takes into account the influence of the roots of the equation 1 - ∫ ℝ e s x F ( d x ) = 0 , F being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace...

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

Klebanov, Lev, Rachev, Svetlozar (1996)

Serdica Mathematical Journal

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* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists. In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum...