arXiv Open Access 2017

Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues

Dmitri Finkelshtein Pasha Tkachov

Lihat Sumber

Abstrak

We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular sub-exponential functions and use it to find an analogue of Kesten's bound for functions on $\mathbb{R}^d$. The results are applied for the study of the fundamental solution to a nonlocal heat-equation.

Topik & Kata Kunci

math.PR math.AP math.CA

Penulis (2)

Dmitri Finkelshtein

Pasha Tkachov

Format Sitasi

APA MLA BibTeX

Finkelshtein, D., Tkachov, P. (2017). Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues. https://arxiv.org/abs/1704.05829

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓