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Approximation by Poisson law

100%

Aleškevičienė A., Statulevičius V.

Discussiones Mathematicae Probability and Statistics

2005

tom 25

nr 2

161-179

We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.

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

72%

Sgibnev M. S.

Studia Mathematica

2000

tom 140

nr 1

41-55

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 $1-∫_ℝe^{sx}F(dx)=0,F$ 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 transforms.

Ograniczanie wyników

1 Discussiones Mathematicae Probability and Statistics

1 Studia Mathematica

1 Aleškevičienė A.

1 Sgibnev M. S.

1 Statulevičius V.

1 2005

1 2000

Wyniki wyszukiwania

Approximation by Poisson law

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