相关论文: An application of multivariate total positivity to…
We investigate positivity properties in quantum field theory (QFT). We provide evidence,and in some case proofs, that many building blocks of scattering amplitudes, and in some cases the full amplitudes, satisfy an infinite number of…
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…
We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional…
We show that several general classes of stochastic processes satisfy a functional co-monotony principle, including processes with independent increments, Brownian diffusions, Liouville processes. As a first application, we recover some…
We provide an equivalent log-concavity condition to the mean residual life (MRL) ordering for real-valued processes. This result, combined with classical properties of total positivity of order 2, allows to exhibit new families of…
The hypercontractivity is proved for the Markov semigroup associated to a class of finite/infinite dimensional stochastic Hamiltonian systems. Consequently, the Markov semigroup is exponentially convergent to the invariant probability…
We study the total positivity of the kernel $1/(x^2 + 2 \cos(\pi\a)xy +y^2).$ The case of infinite order is characterized by an application of Schoenberg's theorem. We then give necessary conditions for the cases of any given finite order…
Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 ($…
A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…
We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The…
The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC…
We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root. By additionally verifying finitely many initial terms, the positivity can also be resolved. As an…
Consider a discrete-time optimal selection problem where one observes a sequence of independent Bernoulli trials and receives a nonnegative reward upon stopping on a success. The aim is to find a single-choice strategy that maximises the…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
Misra, Prigogine and Courbage (MPC) demonstrated the possibility of obtaining stochastic Markov processes from deterministic dynamics simply through a "change of representation" which involves no loss of information provided the dynamical…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…
Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure…
We introduce a family of norms on the $n \times n$ complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in…
Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from…