A large deviations theory for maxitive set functions
The theory of large deviations studies the asymptotic tail behaviour of stochastic processes. This theory arose in the context of ruin theory, while Varadhan and Donsker developed the modern framework of this field. We present a novel approach to large deviations based on maxitive set functions. We introduce a general principle of large deviations for this type of set functions, and systematically generalized and extend the basic results on large deviations to this framework. The theory is illustrated by a series of non-standard large deviation estimators. The talk is based on joint work with Michael Kupper.
References:
M. Kupper, J. M. Zapata, Large deviations built on max-stability, Bernoulli 27(2) (2021)
1001-1027.
M. Kupper, J. M. Zapata, Weakly maxitive set functions and their possibility distributions, Fuzzy Sets and Systems (2023).
Palabras clave: large deviations theory large deviation principle maxitive estimators