Related papers: A bang-bang principle for the conditional expectat…
A vector variational principle is proved.
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
Given a sequence of Borel probability measures on a Hausdorff space which satisfy a large deviation principle, we consider the corresponding sequence of measures formed by conditioning on a set $B$. If the large deviation rate function $I$…
The standard conditional probability definition formula is derived as a consequence of the Insufficient Reason Principle expressed as the Maximum Relative Divergence Principle for grading (order-comonotonic) functions on a totally ordered…
We establish a pre-order principle. From the principle, we obtain a very general set-valued Ekeland variational principle, where the objective function is a set-valued map taking values in a quasi ordered linear space and the perturbation…
Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
Recently, new approaches to adaptive control have sought to reformulate the problem as a minimization of a relative entropy criterion to obtain tractable solutions. In particular, it has been shown that minimizing the expected deviation…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
We first develop a theory of conditional expectations for random variables with values in a complete metric space $M$ equipped with a contractive barycentric map $\beta$, and then give convergence theorems for martingales of…
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…
Identifying covariates that modify treatment effects is a central problem in causal inference. Yet existing data-adaptive procedures do not provide finite-sample control over the expected number of false discoveries, risking spurious…
We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…