Related papers: Infinite Previsions and Finitely Additive Expectat…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
We give some account of investigations for the role of infinite dimensional algebras in time dependent systems.
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
The drawbacks in the formulations of random infinite divisibility in Sandhya (1991, 1996), Gnedenko and Korelev (1996), Klebanov and Rachev (1996), Bunge (1996) and Kozubowski and Panorska (1996) are pointed out. For any given Laplace…
This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…
We reduce the principal problem of Additive Number Theory of whether an infinite sequence of integers constitutes a finite basis for the integers to a Diophantine problem involving the difference set of the sequence, by proving a formula…
We obtain results concerning the so-called factorization for the convergence of random variables almost everywhere (almost surely or with probability one), belonging to the classical Lebesgue-Riesz spaces and we extend these results to the…
We extend the projective covariant bookmaker's bets model to the forecasting gamblers case. The probability of correctness of forecasts shifts probabilities of branching. The formula for the shift of probabilities leads to the velocity…
Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…
We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws…
In this paper we extend to the abstract A-framework some existence theorems for differential inclusion problems with Dirichlet boundary conditions.
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional…