Exponential bounds and tails for additive random recursive sequences
Exponential bounds and tail estimates are derived for additive random recursive sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise as parameters of divide and conquer type algorithms. We derive tail bound...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2007-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/662 |
| _version_ | 1818509091037773824 |
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| author | Ludger Rüschendorf Eva-Maria Schopp |
| author_facet | Ludger Rüschendorf Eva-Maria Schopp |
| author_sort | Ludger Rüschendorf |
| collection | DOAJ |
| description | Exponential bounds and tail estimates are derived for additive random recursive sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise as parameters of divide and conquer type algorithms. We derive tail bounds from estimates of the Laplace transforms and of the moment sequences. For the proof we use some classical exponential bounds and some variants of the induction method. The paper generalizes results of R"osler (% citeyearNP{Roesler:91}, % citeyearNP{Roesler:92}) and % citeN{Neininger:05} on subgaussian tails to more general classes of additive random recursive sequences. It also gives sufficient conditions for tail bounds of the form $exp(-a t^p)$ which are based on a characterization of citeN{Kasahara:78}. |
| first_indexed | 2024-12-10T22:40:44Z |
| format | Article |
| id | doaj.art-b32b47d6b0844c6bbc96a4bff3725774 |
| institution | Directory Open Access Journal |
| issn | 1462-7264 1365-8050 |
| language | English |
| last_indexed | 2024-12-10T22:40:44Z |
| publishDate | 2007-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-b32b47d6b0844c6bbc96a4bff37257742022-12-22T01:30:43ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502007-01-0191Exponential bounds and tails for additive random recursive sequencesLudger RüschendorfEva-Maria SchoppExponential bounds and tail estimates are derived for additive random recursive sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise as parameters of divide and conquer type algorithms. We derive tail bounds from estimates of the Laplace transforms and of the moment sequences. For the proof we use some classical exponential bounds and some variants of the induction method. The paper generalizes results of R"osler (% citeyearNP{Roesler:91}, % citeyearNP{Roesler:92}) and % citeN{Neininger:05} on subgaussian tails to more general classes of additive random recursive sequences. It also gives sufficient conditions for tail bounds of the form $exp(-a t^p)$ which are based on a characterization of citeN{Kasahara:78}.http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/662 |
| spellingShingle | Ludger Rüschendorf Eva-Maria Schopp Exponential bounds and tails for additive random recursive sequences Discrete Mathematics & Theoretical Computer Science |
| title | Exponential bounds and tails for additive random recursive sequences |
| title_full | Exponential bounds and tails for additive random recursive sequences |
| title_fullStr | Exponential bounds and tails for additive random recursive sequences |
| title_full_unstemmed | Exponential bounds and tails for additive random recursive sequences |
| title_short | Exponential bounds and tails for additive random recursive sequences |
| title_sort | exponential bounds and tails for additive random recursive sequences |
| url | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/662 |
| work_keys_str_mv | AT ludgerruschendorf exponentialboundsandtailsforadditiverandomrecursivesequences AT evamariaschopp exponentialboundsandtailsforadditiverandomrecursivesequences |