منابع مشابه
Upper and Lower Bounds in Exponential Tauberian Theorems
In this text we study, for positive random variables, the relation between the behaviour of the Laplace transform near infinity and the distribution near zero. A result of De Bruijn shows that E(e−λX) ∼ exp(rλ) for λ → ∞ and P (X ≤ ε) ∼ exp(s/ε) for ε ↓ 0 are in some sense equivalent (for 1/α = 1/β + 1) and gives a relation between the constants r and s. We illustrate how this result can be use...
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The Abelian and Tauberian-type theorems were introduced by Stanković [7] and Pilipović et al. [5]. In the first part of this paper, we give the definition of the quasiasymptotic expansion at 0+ and the quasiasymptotic behaviour of distributions at infinity from S′+ introduced in [1]. In this paper, we give the definition of space L′(r), classical Stieltjes transformation, modified Stieltjes tra...
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Introduction. The sums formed from the set of non-negative powers of 2 are just the non-negative integers. It is easy to obtain “abelian” results to the effect that if a set is distributed like the powers of 2, then the sum set will be distributed like Dhe non-negative integers. We will be concerned here with converse, or “Tauberian” results. The main theme of this paper is t’he following quest...
متن کاملTauberian Theorems for Summability Transforms
we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...
متن کاملRegularization of Divergent Series and Tauberian Theorems
The concepts of convergence and divergence, while not defined explicitly until early 19th century, have been studied since the third century BC. Throughout this time, mathematicians have largely focused upon convergent sequences and series, having seemingly little analytical reason to study series that diverged. However, as the area of mathematical analysis developed over the past few centuries...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1978
ISSN: 2156-2261
DOI: 10.1215/kjm/1250522571