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Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
Dmitri Finkelshtein 
,
Pasha Tkachov
,
Pasha Tkachov
Advances in Applied Probability, Volume: 50, Issue: 02, Pages: 373 - 395
Swansea University Author:
Dmitri Finkelshtein
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DOI (Published version): 10.1017/apr.2018.18
Abstract
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...
| Published in: | Advances in Applied Probability |
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| ISSN: | 0001-8678 1475-6064 |
| Published: |
Applied Probability Trust/Cambridge University Press
2018
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa38336 |
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| Abstract: |
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 R^d. The results are applied for the study of the fundamental solution to a nonlocal heat-equation. |
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| Keywords: |
sub-exponential densities; long-tail functions; heavy-tailed distributions; convolution tails; tail-equivalence; asymptotic behavior |
| College: |
Faculty of Science and Engineering |
| Issue: |
02 |
| Start Page: |
373 |
| End Page: |
395 |