Precise Laplace-Type Asymptotics for Moderate Deviations of the Distributions of Sums of Independent Banach-Valued Random Elements
Copyright policy )Precise Laplace-Type Asymptotics for Moderate Deviations of the Distributions of Sums of Independent Banach-Valued Random Elements
The author considers the possibility of applying the Laplace method to find exact asymptotics of moderate deviations of sums of independent identically distributed Banach-valued random elements. This method is an extension of the classical asymptotic Laplace method to the case of integrals with respect to probability measures in infinite-dimensional Banach spaces. Moreover he deduces a new formula for the exact asymptotics for the probabilities of moderate deviations of the statistics of type \(\omega^p_n\), \(p\geqslant2\).
probabilities of moderate deviations of statistics of the form \(\omega^p_n\), Large deviations, sums of independent random elements, Probabilistic methods in Banach space theory, Laplace method in Banach spaces, Probability theory on algebraic and topological structures
probabilities of moderate deviations of statistics of the form \(\omega^p_n\), Large deviations, sums of independent random elements, Probabilistic methods in Banach space theory, Laplace method in Banach spaces, Probability theory on algebraic and topological structures
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