相关论文: Monotone and Boolean Convolutions for Non-compactl…
One possible natural monotone version of countable paracompactness, MCP, turns out to have some interesting properties. We investigate various other possible monotonizations of countable paracompactness and how they are related.
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Characterization and quantification of multipartite entanglement is one of the challenges in state-of-the-art experiments in quantum information processing. According to theory, this is achieved via entanglement monotones, that is,…
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
We discuss the recently introduced concept of non-deterministic noiseless linear amplification, demonstrating that such an operation can only be performed perfectly with vanishing probability of success. We show that a weak measurement,…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…
Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…
The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence…
We study sub-semigroups of the semigroup of probability measures on $\mathbb{R}$ and monotone additive statistics on them, by which we mean maps to the reals that are monotone with respect to the stochastic order and additive under…
Given a probability measure $\mu$ on the real line, there exists a semigroup $\mu_t$ with real parameter $t>1$ which interpolates the discrete semigroup of measures $\mu_n$ obtained by iterating its free convolution. It was shown in…
We study (weakly) continuous convolution semigroups of probability measures on a Lie group G or a homogeneous space G/K, where K is a compact subgroup. We show that such a convolution semigroup is the convolution product of its initial…
We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…
Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n^{-1/2}, the same as in the classical case.…