相关论文: Measure convolution semigroups and non-infinitely …
A metric measure space is a complete separable metric space equipped with probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on…
The free convolution is the binary operation on the set of probability measures on the real line which allows to deduce, from the individual spectral distributions, the spectral distribution of a sum of independent unitarily invariant…
A companion paper develops a framework in which probability measures are represented by distribution-kernel pairs (T,phi) with T a tempered distribution and phi a Schwartz kernel, so that weak moments of all orders exist unconditionally.…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
The Bayesian framework is ideally suited for induction problems. The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes' rule if the true distribution $\mu$ of the sequences…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
The Glivenko--Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges to the underlying distribution (in the sense of uniform…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
We derive new explicit bounds for the total variation distance between two convolution products of $n$ probability distributions, one of which having identical convolution factors. Approximations by finite signed measures of arbitrary order…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising…
A quasi-infinitely divisible distribution on $\mathbb{R}^d$ is a probability distribution $\mu$ on $\mathbb{R}^d$ whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
We consider the free additive convolution semigroup $\lbrace \mu^{\boxplus t}:\,t\ge 1\rbrace$ and determine the local behavior of the density of $\mu^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study…
We prove that there exists a diffusion process whose invariant measure is the three dimensional polymer measure $\nu_\lambda$ for all $\lambda>0$. We follow in part a previous incomplete unpublished work of the first named author with M.…
This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of…