Related papers: Law-invariant functionals that collapse to the mea…
The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
A class of real functions, which is the generalization of a family of convex functions, is introduced; in this connection, we have defined $X$-convex, strictly $X$-convex, quasi-$X$-convex, strictly quasi-$X$-convex, and semi-strictly…
Geometrically convex functions constitute an interesting class of functions obtained by replacing the arithmetic mean with the geometric mean in the definition of convexity. As recently suggested, geometric convexity may be a sensible…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
We study a counterfactual mean-variance optimization, where the mean and variance are defined as functionals of counterfactual distributions. The optimization problem defines the optimal resource allocation under various constraints in a…
Under appropriate integrability conditions the risk measure of the sample measures for a law invariant risk measure converge almost surely to the risk measure of the sampled random variable. The results follow from general convergence…
We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We extend…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
In a seminal paper, Choquet introduced an integral formula to extend a monotone increasing setfunction on a sigma-algebra to a (nonlinear) functional on bounded measurable functions. The most important special case is when the setfunction…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
The mean value inequality is characteristic for upper semicontinuous functions to be subharmonic. Quasinearly subharmonic functions generalize subharmonic functions. We find the necessary and sufficient conditions under which subsets of…
The classic Reinforcement Learning (RL) formulation concerns the maximization of a scalar reward function. More recently, convex RL has been introduced to extend the RL formulation to all the objectives that are convex functions of the…
In this paper, we explore the concept of $\sigma$-quasiconvexity for functions defined on normed vector spaces. This notion encompasses two important and well-established concepts: quasiconvexity and strong quasiconvexity. We start by…
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…