Displaying similar documents to “An asymptotic series expansion of the multidimensional renewal measure”

On the fractional parts of x / n and related sequences. I

Bahman Saffari, R. C. Vaughan (1976)

Annales de l'institut Fourier

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This paper and its sequels deal with a new concept of distributions modulo one which is connected with the Dirichlet divisor and similar problems. Each of the theorems has some independent interest, and in addition some of the techniques developed lead to improvements in certain applications of the hyperbola method.

On the theorem of Ivasev-Musatov. II

Thomas-William Korner (1978)

Annales de l'institut Fourier

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As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.

The distribution of the sum-of-digits function

Michael Drmota, Johannes Gajdosik (1998)

Journal de théorie des nombres de Bordeaux

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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.

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...