Statistics & Probability Letters最新文献

In this paper, we study general mean-field reflected backward stochastic differential equations with locally monotone coefficients. With the help of choosing the suitable approximation sequence, we obtain the existence and uniqueness of solution to general mean-field reflected backward stochastic differential equations.

We generalize a strong form of the three-dimensional Gaussian product inequality studied by Herry et al. (2024), who resolved the case of any triple of even positive integers. We extend the result to any triple consisting of a pair of positive real numbers and an even positive integer. Our result includes all existing results on the three-dimensional Gaussian product inequality conjecture.

We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature. From our Stein characterisation we derive recursive formulas for the moments of the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, which allows for efficient computation of higher order moments.

Distribution continuity is established for extremes of Gaussian processes with bounded sample paths and positive variance or continuous sample paths over compact domain, and for multiparameter Brownian sheets. These results provide probabilistic support for global inference on unknown functions.

Although the Hawkes process has been widely applied, their probability properties are difficult to obtain, depending on the model structure. This paper proposes a multivariate Hawkes process, which allows for common jumps from each marginal processes. The probability of this common jump is determined by another independent process, which represents the arrival intensity of external shocks to the system. The infinitesimal generator of the new multivariate jump process is derived. Based on that, moments and the Laplace transform are studied, which further demonstrate the advantages of this model structure.

We discuss a representation of any probability distribution on the set of non-negative integers as a waiting time distribution in a sequence of independent Bernoulli trials. Several associated results are derived and illustrated by examples. Multivariate extensions are briefly treated as well.

In this paper, we focus on investigating the asymptotic behavior of solutions in a mean square sense to bilinear Caputo stochastic fractional differential equations (CSFDEs). The main tools in the proof include a variation of the constant formula for CSFDEs, the Jordan normal form of a matrix, the summation formula of Djrbashian type, and constructing a weighted norm in the associated Banach space.

Let $\left(Z_n\right)$ be a supercritical branching process in an independent and identically distributed (i.i.d.) random environment. The paper studies the properties of the estimator $M_n=n^{-1}{\sum }_{k=0}^{n-1}(Z_{k+1}/Z_k)$ introduced by Dion and Esty in 1979. We introduce a related martingale and discuss its convergence and exponential convergence rate. On this basis the exact convergence rate of the central limit theorem for normalized $M_n$ is given.

The win-ratio analysis of controlled clinical trials uses pairwise comparisons between patients in the treatment and control group based on a primary outcome, say time to death, with indeterminacies resolved where possible by a secondary outcome, say time to hospitalization. The resulting preferences may not be transitive. Intransitivity occurs when potential follow-up times vary between patients and rankings from the primary events differ from those from secondary events. We characterize the structure of closed loops, derive some general properties of win-ratio preferences and provide simple numerical illustrations. Under realistic assumptions, unless all potential follow-up times are equal, intransitivities are certain to occur in sufficiently large samples, but their overall frequency is low.