We show that quasi-every Brownian path in R (with respect to an Ornstein-Uhlenbeck process in the space of paths) has level sets of Hausdorff dimension 1 2 , for all levels, and quasi-every planar Brownian motion has ...
详细信息
We show that quasi-every Brownian path in R (with respect to an Ornstein-Uhlenbeck process in the space of paths) has level sets of Hausdorff dimension 1 2 , for all levels, and quasi-every planar Brownian motion has a set of r -multiple points of dimension 2 for arbitrary finite r .
A random sample size version of the central limit theorem is obtained for a general class of symmetric statistics based on uniform spacings. An important application to goodness of fit test for a Poisson process is di...
详细信息
A random sample size version of the central limit theorem is obtained for a general class of symmetric statistics based on uniform spacings. An important application to goodness of fit test for a Poisson process is discussed.
Graph Neural Networks (GNNs) have demonstrated remarkable success in various applications, yet they often struggle to capture long-range dependencies (LRD) effectively. This paper introduces GraphMinNet, a novel GNN a...
详细信息
Let X, Y and Z be independent random variables with common unknown distribution F. Using the Dirichlet process prior for F and squared erro loss function, the Bayes and empirical Bayes estimators of the parameters λ(...
详细信息
Let X, Y and Z be independent random variables with common unknown distribution F. Using the Dirichlet process prior for F and squared erro loss function, the Bayes and empirical Bayes estimators of the parameters λ(F). the probability that Z > X + Y, are derived. The limiting Bayes estimator of λ(F) under some conditions on the parameter of the process is shown to be asymptotically normal. The aysmptotic optimality of the empirical Bayes estimator of λ(F) is established. When X, Y and Z have support on the positive real line, these results are derived for randomly right censored data. This problem relates to testing whether than used discussed by Hollander and Proshcan (1972) and Chen, Hollander and Langberg (1983).
Letbe a Markov chain with state space inR+= (0,∞), an initial distributionμand a transition probabilityQ. For eachx∊R+the support ofis [0,x], which implies that. Setand put. We prove thatis a Markov renewal process ...
Letbe a Markov chain with state space inR+= (0,∞), an initial distributionμand a transition probabilityQ. For eachx∊R+the support ofis [0,x], which implies that. Setand put. We prove thatis a Markov renewal process and thatis a Markov process with a stationary transition probability function. Writeand suppose that. We give conditions under whichis relatively stable and show that, whereare stabilizing constants andZis exponentially distributed. We also show thatis asymptotically stationary and possesses a mixing property
Let X 1 , X 2 ,…, be i.i.d. random variables, which are uniformly distributed on [0,1]. Further let I 1 (0) = [0, 1] and let I k ( n ) denote the k th largest interval generated by the points 0, X 1 , X 2 ,…, X n −1...
详细信息
Let X 1 , X 2 ,…, be i.i.d. random variables, which are uniformly distributed on [0,1]. Further let I 1 (0) = [0, 1] and let I k ( n ) denote the k th largest interval generated by the points 0, X 1 , X 2 ,…, X n −1 , 1 (or equivalently, the interval corresponding to the k th largest spacing at the n th stage). This note studies the question for which classes of sequences k = k ( n ), will the interval I k ( n ) ( n ) be hit (a.s.) only finitely often, as well as infinitely often.
In applications, considerations on stochastic models often involve a Markov chain [formula omitted] with state space in R+, and a transition probability Q. For each x ε R+ the support of Q(x,) is [0, x]. This implies...
详细信息
A nonparametric formulation is set up for selecting the best one of k populations. “Best” is defined as the one with the smallest inter(a,e)-range, a measure of dispersion defined by the difference of the 6th quanti...
详细信息
This paper introduces a method for pricing insurance policies using market data. The approach is designed for scenarios in which the insurance company seeks to enter a new market, in our case: pet insurance, lacking h...
详细信息
We study a class of stationary sequences having spectral representation (M(tau(n)A))n is-an-element-of z, where A is a set in a measure space (E, E, mu), tau is an invertible measure-preserving transformation on (E, E...
详细信息
We study a class of stationary sequences having spectral representation (M(tau(n)A))n is-an-element-of z, where A is a set in a measure space (E, E, mu), tau is an invertible measure-preserving transformation on (E, E, mu), and M is a random measure on (E, E, mu). We explore the relationship between the ergodic properties of the sequence and the properties of tau, and construct examples with various ergodic properties using a stacking method on the half-line [0, infinity).
暂无评论