Browsing by Subject "Large deviations"

Now showing 1 - 3 of 3
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    Boolean valued representation of random Sets and markov kernels with application to large deviations
    (MDPI, 2020-10-20) Avilés López, Antonio; Estadística e Investigación Operativa
    We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a Boolean valued model. This enables a Boolean valued transfer principle to obtain random set analogues of available theorems. As an application, we establish a Boolean valued transfer principle for large deviations theory, which allows for the systematic interpretation of results in large deviations theory as versions for Markov kernels. By means of this method, we prove versions of Varadhan and Bryc theorems, and a conditional version of Cramér theorem.
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    Large deviations built on max-stability
    (2021-05) Kupper, Michael; Estadística e Investigación Operativa
    In this paper, we show that the basic results in large deviations theory hold for general monetary risk measures, which satisfy the crucial property of max-stability. A max-stable monetary risk measure fulfills a lattice homomorphism property, and satisfies under a suitable tightness condition the Laplace Principle (LP), that is, admits a dual representation with affine convex conjugate. By replacing asymptotic concentration of probability by concentration of risk, we formulate a Large Deviation Principle (LDP) for max-stable monetary risk measures, and show its equivalence to the LP. In particular, the special case of the asymptotic entropic risk measure corresponds to the classical Varadhan–Bryc equivalence between the LDP and LP. The main results are illustrated by the asymptotic shortfall risk measure.
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    Representation of weakly maxitive monetary risk measures and their rate functions
    (Elsevier, 2023-01-31) Zapata García, José Miguel; Estadística e Investigación Operativa
    This article provides a representation result for monetary risk measures (i.e., monotone translation-invariant functionals) satisfying a weak maxitivity property. This result can be understood as a functional analytic generalization of the Gärtner-Ellis large deviations theorem. In contrast to the classical Gärtner-Ellis theorem, the rate function is computed on an arbitrary set of continuous real-valued functions rather than the dual space. As an application of the main result, we establish a large deviations result for sequences of sublinear expectations on regular Hausdorff topological spaces.