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Register a new userLarge deviation results for triangular arrays of semiexponential random variables
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Asymptotics deviation probabilities of the sum S n = X 1 + $times$ $times$ $times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated , in particular when X 1 is not exponentially integrable. For instance, A.V. Nagaev formulated exact asymptotics results for P(S n > x n) when X 1 has a semiexponential distribution (see, [16, 17]). In the same setting, the authors of [4] derived deviation results at logarithmic scale with shorter proofs relying on classical tools of large deviation theory and expliciting the rate function at the transition. In this paper, we exhibit the same asymptotic behaviour for triangular arrays of semiexponentially distributed random variables, no more supposed absolutely continuous.
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Asymptotics deviation probabilities of the sum S n = X 1 + $times$ $times$ $times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated, in particular when X 1 is not exponentially integrable. For instance, A.V. Nagaev formulated exact asymptotics results for P(S n > x n) when x n > n 1/2 (see, [13, 14]). In this paper, we derive rough asymptotics results (at logarithmic scale) with shorter proofs relying on classical tools of large deviation theory and expliciting the rate function at the transition.
We consider the branching process in random environment ${Z_n}_{ngeq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We describe precise asymptotics of upper large deviations, i.e. $mathbb{P}[Z_n > e^{rho n}]$. Moreover in the subcritical case, under the Cramer condition on the mean of the reproduction law, we investigate large deviations-type estimates for the first passage time of the branching process in question and its total population size.
Borgs, Chayes, Gaudio, Petti and Sen [arXiv:2007.14508] proved a large deviation principle for block model random graphs with rational block ratios. We strengthen their result by allowing any block ratios (and also establish a simpler formula for the rate function). We apply the new result to derive a large deviation principle for graph sampling from any given step graphon.
We derive properties of the rate function in Varadhans (annealed) large deviation principle for multidimensional, ballistic random walk in random environment, in a certain neighborhood of the zero set of the rate function. Our approach relates the LDP to that of regeneration times and distances. The analysis of the latter is possible due to the i.i.d. structure of regenerations.
In this paper, we are concerned with SIR epidemics in a random environment on complete graphs, where every edges are assigned with i.i.d. weights. Our main results give large and moderate deviation principles of sample paths of this model.
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