On Estimation of Poisson Intensity Functions

Under the presence of only one realization, we consider a computationally simple algorithm for estimating the intensity function of a Poisson process with exponential quadratic and cyclic of fixed frequency trends. We argue that the algorithm can successfully be used to estimate any Poisson intensity function provided that it has a parametric form.     

An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Let e _t=(e _t1,...e _tp) be a p-dimensional nonnegative strict white noise with finite second moments. Let h _ij(x) be nondecreasing functions from [0,) onto [0,) such that h _ij(x) x for i, j = 1,...,p. Let U = (u _ij) be a p×p matrix with nonnegative elements having all its roots inside the unit circle. Define a process X t=(X _t1,...,X _tp) by for

An Ergodic Process of Zero Divergence-Distance from the Class of All Stationary Processes

An ergodic process Q is constructed such that the divergence-rate D(P Q) is zero for all stationary processes P. The process Q is constructed using the cutting and stacking method.     

A General Lower Bound for Gaussian Chaos

We give in full generality a lower bound for the expected value of the supremum of a chaos process indexed by a set T, in terms of the structure of T for the two natural distances induced by the process.     

正态过程逼近随机过程研究

讨论正态过程中的一个重要特例维纳过程，对正态过程的特性和它逼近随机过程的机制原理做出一定的分析研究。     

Weibull renewal processes

We study the class of renewal processes with Weibull lifetime distribution from the point of view of the general theory of point processes. We investigate whether a Weibull renewal process can be expressed as a Cox process. It is shown that a Weibull renewal process is a Cox process if and only if 0<1, where denotes the shape parameter of the Weibull distribution. The Cox character of the process is analyzed. It is shown that the directing measure of the process is continuous and singular.     

Semi-Selfsimilar Processes

A notion of semi-selfsimilarity of R ^d -valued stochastic processes is introduced as a natural extension of the selfsimilarity. Several topics on semi-selfsimilar processes are studied: the existence of the exponent for semi-selfsimilar processes; characterization of semi-selfsimilar processes as scaling limits; relationship between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, and examples; construction of semi-selfsimilar processes with stationary increments; and extension of the Lamperti transformation. Semi-stable processes where all joint distributions are multivariate semi-stable are also discussed in connection with semi-selfsimilar processes. A wide-sense semi-selfsimilarity is defined and shown to be reducible to semi-selfsimilarity.     

全稳定Q过程构造的一个等价条件

给出了Q过程构造的等价条件,证明了Q过程的构造等价于一个条件方程组的解,以此方法求出了所有的Q过程、F过程、B过程及BF过程的等价条件。     

Markov process functionals in finance and insurance

The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained： the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.     

The largest table in Chinese restaurant processes

In this paper, we investigate the expectation of the size of the largest table in an (α, θ)-Chinese restaurant process by using and developing an idea originated in the work by Shepp, which discusses random permutation. This work was supported by National Natural Science Foundation of China (Grant No. 10671036) and the National Basic Research Program of China (Grant No. 2007CB814904)     

On risk processes with the Markov property and with independent increments

We study the influence on the underlying counting process of the Markov property and of the property of independent increments for a risk process.     

混合过程的刻画

研究了接触过程和非紧邻的排它过程的混合过程,得到混合过程除在临界点λc(β)处外,它的平稳分布总是光滑的,并且混合过程有一定的稳定性.     

Stochastic order for alpha-permanental point processes

We establish relations of stochastic comparison among point processes elements of the set of alpha-permanental point processes. This set contains in particular, the determinantal point processes, the Poisson point processes and the permanental point processes. We show that these three classes of point processes can be ordered according to the increasing stochastic order. Elementary particles provide illustrations of some of the obtained relations of stochastic comparison.     

What is a multi-parameter renewal process?

The concept of the renewal property is extended to processes indexed by a multidimensional time parameter. The definition given includes not only partial sum processes, but also Poisson processes and many other point processes whose jump points are not totally ordered. A new version of the waiting time paradox is proven for multidimensional Poisson processes, and is shown to imply the renewal property. Finally, martingale properties of renewal processes are studied.     

Can We Bootstrap Even if CLT Fails?

It is shown that in some cases the bootstrap in probability holds under conditions weaker than necessary for the original empirical Central Limit Theorem.     

Semi-Markov failure rates processes

Usually, a reliability function is defined by a failure rate which is a real function taking the non-negative real values. In this paper the failure rate is assumed to be a stochastic process with non-negative and right continuous trajectories. The reliability function is defined as an expectation of a function of that random process. Particularly, the failure rate defined by the semi-Markov processes is considered here. The theorems dealing with the renewal equations for the conditional reliability functions with a semi-Markov process as a failure rate are presented in this paper. A system of that kind of equations for the discrete state space semi-Markov process is applied for calculating the reliability function for the 3-states semi-Markov random walk. Using the introduced system of renewal equations for the countable state space, the reliability function for the Furry-Yule failure rate process is obtained.     

Continuous random walks and fractional powers of operators

We derive a probabilistic representation for the Fourier symbols of the generators of some stable processes. This short paper represents a bridge between probabilists and researchers working in PDE?s.     

Thinning of point processes,revisited

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