Abstract We extend two characterizations of admissible operators with respect to $$\textrm{L}^p$$ L p more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly continuous semigroup and in terms...

We propose a general framework for the study of L1 contractive semigroups of solutions to conservation laws with discontinuous flux: ut + f(x, u)x = 0, f(x, u) = ( f (u), x < 0, f(u), x > 0, (CL) where the fluxes f , f are mainly assumed to be continuous. Developing the ideas of a number of preceding works (Baiti and Jenssen [14], Audusse and Perthame [12], Garavello et al. [35], Adimurthi et a...

This paper modifies the Wald development of statistical decision theory to offer new perspective on the performance of certain statistical treatment rules. We study the quantile performance of test rules, ones that use the outcomes of hypothesis tests to allocate a population to two treatments. Let λ denote the quantile used to evaluate performance. Define a test rule to be λ-quantile optimal i...

In this paper we study the relationship between the notion of coherence for conditional probability assessments on a family of conditional events and the notion of admissibility with respect to scoring rules. By extending a recent result given in literature for unconditional events, we prove, for any given strictly proper scoring rule s, the equivalence between the coherence of a conditional pr...