Related papers: Cubature rules and expected value of some complex …
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
In this article, we discuss a novel approach to solving number sequence problems, in which sequences of numbers following unstated rules are given, and missing terms are to be inferred. We develop a methodology of decomposing test sequences…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…
This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \(\xiv\) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The…
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
An intricate quantum statistical effect guides us to a deterministic, non-causal quantum universe with given fixed initial and final state density matrix. A concept is developed on how and where something like macroscopic physics can…
We study a class of hypothesis testing problems in which, upon observing the realization of an $n$-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…
The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…
The Regge calculus generalised to independent area tensor variables is considered. The continuous time limit is found and formal Feynman path integral measure corresponding to the canonical quantisation is written out. The quantum measure…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
High dimensional integrals can be approximated well by quasi-Monte Carlo methods. However, determining the number of function values needed to obtain the desired accuracy is difficult without some upper bound on an appropriate semi-norm of…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
In the classic scoring rule setting, a principal incentivizes an agent to truthfully report their probabilistic belief about some future outcome. This paper addresses the situation when this private belief, rather than a classical…
The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
We prove a formula for the evaluation of expectations containing a scalar function of a Gaussian random vector multiplied by a product of the random vector components, each one raised to a non-negative integer power. Some of the powers…