ASYMPTOTIC FORMULAS FOR PROBABILITIES OF LARGE DEVIATIONS OF LADDER HEIGHTS

SERGEY V. NAGAEV

Theory of Stochastic Processes Vol. 14 (30), no. 1, 2008, pp. 100–116

Asymptotic formulas for large-deviation probabilities of a ladder height in a random walk generated by a sequence of sums of i.i.d. random variables are deduced.
Two cases are considered:

a) the distribution $F(x)$ of summands is normal with a zero
mean.

b) $F(x)$ belongs to the domain of the normal attraction of a stable law with the exponent $0<\alpha<1.$

The method of Laplace transforms is applied in proofs.

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