Establishes a uniform Tauberian theorem yielding precise large deviation principles for stable attraction basins, covering long-memory walks and infinite-mean stopping times.
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Extension of the Tauberian method to bivariate transforms yields precise large-deviation asymptotics for processes in the domain of attraction of spectrally positive stable laws, illustrated on correlated random sums and positive random walks.
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Precise large deviations through a uniform Tauberian theorem
Establishes a uniform Tauberian theorem yielding precise large deviation principles for stable attraction basins, covering long-memory walks and infinite-mean stopping times.
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Double-transform Tauberian method for precise large deviations
Extension of the Tauberian method to bivariate transforms yields precise large-deviation asymptotics for processes in the domain of attraction of spectrally positive stable laws, illustrated on correlated random sums and positive random walks.