Large deviations for heavy-tailed random sums in compound renewal model

By Qihe Tang, C. Su, Tao Jiang, Jinsong Zhang. 2001

123 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/39dd1aec1cf91e67d47213cec7323c31a2852ad2

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Citations in the corpus

Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation (2011, methodology): “}, one can follow the proof of Lemma 3.5 of Tang et al. (2001) and use Lemma 2.2 of Tang (2006) to show that, for every fixed p > 0 and δ> 0, �”
Precise large deviations for sums of random variables with consistently varying tails (2004, methodology): “This assumption is satisfied, for example, by the renewal counting process as verified in Lemma 3.5 of Tang et al. (2001).”
Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails (2002, unknown): “F ∈ ERV(−α, −β) for 1 < α ≤ β < ∞, i.e. ≤ v −α for any v > 1, then F satisfies all the conditions in Proposition 4.1, see Bingham et al. (1987) and Tang et al. (2001) for details.”
Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails (2010, background): “Tang et al. [ 22 ] weakened conditions (A1) and (A2) to the one that for some p>β and all δ> 0,”
Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models (2007, background): “For more details on regularly varying tails and extended regularly varying tails, see Klüppelberg and Mikosch (1997) or Tang et al. (2001).”
Insensitivity to Negative Dependence of the Asymptotic Behavior of Precise Large Deviations (2006, background): “…Nagaev (1969a, 1969b, 1969c), S.V. Nagaev (1973, 1979), Pinelis (1985), while for recent works, we refer to Cline and Hsing (1991), Rozovskĭı (1993), Vinogradov (1994), Mikosch and A.V. Nagaev (1998), Tang et al. (2001), Ng et al. (2004), and Baltrūnas and Klüppelberg (2004), among many others.”
A property of the renewal counting process with application to the finite-time ruin probability (2009, background): “In addition, Tang et al. ([ 11 ], Lemma 3.5) proved that if Θ(t) is a renewal counting process with Eθ = 1/λ < ∞, then, for any positive real constants δ and m,”