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On subadditive functions and ψ-additive mappings

100%

Matkowski J.

Open Mathematics

2003

tom 1

nr 4

435-440

In [4], assuming among others subadditivity and submultiplicavity of a function ψ: [0, ∞)→[0, ∞), the authors proved a Hyers-Ulam type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed conditions of the function ψ imply that ψ=0 and, consequently, every “ψ-additive” mapping must be additive

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 Open Mathematics

1 Studia Mathematica

1 Matkowski J.

1 Sgibnev M. S.

1 2003

1 2000

Wyniki wyszukiwania

On subadditive functions and ψ-additive mappings

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