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A note on randomly stopped sums with zero mean increments
Modern Stochastics: Theory and Applications, 2023 In this paper, the asmptotics is considered for the distribution tail of a randomly stopped sum ${S_{\nu }}={X_{1}}+\cdots +{X_{\nu }}$ of independent identically distributed consistently varying random variables with zero mean, where ν is a counting ...
Remigijus Leipus, Jonas Šiaulys
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Asymptotics of the occupancy scheme in a random environment and its applications to tries [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Consider $ m $ copies of an irreducible, aperiodic Markov chain $ Y $ taking values in a finite state space. The asymptotics as $ m $ tends to infinity, of the first time from which on the trajectories of the $ m $ copies differ, have been studied by ...
Silvia Businger
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Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 66, Page 3565-3576, 2004., 2004 Let {X, Xn; n ≥ 1} be a sequence of real‐valued i.i.d. random variables and let Sn=∑i=1nXi, n ≥ 1. In this paper, we study the probabilities of large deviations of the form P(Sn > tn1/p), P(Sn < −tn1/p), and P(|Sn| > tn1/p), where t > 0 and 0 < p < 2.
Deli Li, Andrew Rosalsky
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Upper tails for triangles [PDF]
, 2010 With $\xi$ the number of triangles in the usual (Erd\H{o}s-R\'enyi) random graph $G(m,p)$, $p>1/m$ and $\eta>0$, we show (for some $C_{\eta}>0$) $$\Pr(\xi> (1+\eta)\E \xi) < \exp[-C_{\eta}\min{m^2p^2\log(1/p),m^3p^3}].$$ This is tight up to the value of $
Alon +10 more
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Analysis of statistical equilibrium models of geostrophic turbulence
International Journal of Stochastic Analysis, Volume 15, Issue 4, Page 327-347, 2002., 2002 Statistical equilibrium lattice models of coherent structures in geostrophic turbulence, formulated by discretizing the governing Hamiltonian continuum dynamics, are analyzed. The first set of results concern large deviation principles (LDP′s) for a spatially coarse‐grained process with respect to either the canonical and/or the microcanonical ...
Richard S. Ellis +2 more
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International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 3, Page 481-497, 1992., 1992 Let X, Xn, n ≥ 1 be a sequence of iid real random variables, and , n ≥ 1. Convergence rates of moderate deviations are derived, i.e., the rate of convergence to zero of certain tail probabilities of the partial sums are determined. For example, we obtain equivalent conditions for the convergence of series only under the assumptions convergence that EX =
Deli Li, Xiangchen Wang, M. Bhaskara Rao
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Large deviation asymptotics for continued fraction expansions [PDF]
, 2007 We study large deviation asymptotics for processes defined in terms of continued fraction digits. We use the continued fraction digit sum process to define a stopping time and derive a joint large deviation asymptotic for the upper and lower fluctuation ...
Kesseböhmer, Marc, Slassi, Mehdi
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Edgeworth expansions in operator form [PDF]
, 2007 An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method.
Gnedenko +10 more
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Local Large deviation: A McMillian Theorem for Coloured Random Graph Processes
, 2017 For a finite typed graph on $n$ nodes and with type law $\mu,$ we define the so-called spectral potential $\rho_{\lambda}(\,\cdot,\,\mu),$ of the graph.From the $\rho_{\lambda}(\,\cdot,\,\mu)$ we obtain Kullback action or the deviation function ...
Doku-Amponsah, Kwabena
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Large deviations for the rightmost position in a branching Brownian motion
, 2017 We study the lower deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its large deviation ...
Derrida, Bernard, Shi, Zhan
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