https://hal.inria.fr/hal-00964242Rüschendorf, LudgerLudgerRüschendorfMathematisches Institut [Freiburg] - Albert-Ludwigs-Universität FreiburgSchopp, Eva-MariaEva-MariaSchoppMathematisches Institut [Freiburg] - Albert-Ludwigs-Universität FreiburgExponential bounds and tails for additive random recursive sequencesHAL CCSD2007[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-Méditerranée / I3s, Service Ist2014-03-24 11:13:392017-11-29 10:26:182014-03-25 11:05:05enJournal articleshttps://hal.inria.fr/hal-00964242/document10.46298/dmtcs.408application/pdf1Exponential 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 Rösler (% \citeyearNPRoesler:91, % \citeyearNPRoesler:92) and % \citeNNeininger: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 \citeNKasahara:78.