THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS

The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.     

Asymptotic Expansions of Transition Densities for Hybrid Jump-diffusions

A class of hybrid jump diffusions modulated by a Markov chain is considered in this work.Themotivation stems from insurance risk models,and emerging applications in production planning and wirelesscommunications.The models are hybrid in that they involve both continuous dynamics and discrete events.Under suitable conditions,asymptotic expansions of the transition densities for the underlying processes aredeveloped.The formal expansions are validated and the error bounds obtained.     

Smooth Scalar-on-Image Regression via Spatial Bayesian Variable Selection

We develop scalar-on-image regression models when images are registered multidimensional manifolds. We propose a fast and scalable Bayes’ inferential procedure to estimate the image coefficient. The central idea is the combination of an Ising prior distribution, which controls a latent binary indicator map, and an intrinsic Gaussian Markov random field, which controls the smoothness of the nonzero coefficients. The model is fit using a single-site Gibbs sampler, which allows fitting within minutes for hundreds of subjects with predictor images containing thousands of locations. The code is simple and is provided in the online Appendix (see the “Supplementary Materials” section). We apply this method to a neuroimaging study where cognitive outcomes are regressed on measures of white-matter microstructure at every voxel of the corpus callosum for hundreds of subjects.     

马氏风险过程

研究了一般马氏风险过程,它是经典风险过程的拓广．具有大额索赔的风险过程用此马氏风险模型来描述是适合的．在此模型中,索赔到达过程由一点过程来描述,该点过程是一马氏跳过程从0到t时间段内的跳跃次数．主要研究了此风险模型的破产概率,得到了破产概率满足的积分方程,并应用本文引入的广更新方法,得到了破产概率的收敛速度上界．     

ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS

In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...     

Probability of a major infection in a stochastic within-host model with multiple stages

Establishment or spread of a viral infection within healthy individuals depends on exposure to a viral source, either through virus particles or through cells that have been infected. We assume that a potential infection has reached the site of the healthy target cells and we apply stochastic within-host models and multitype branching processes to investigate whether a major infection becomes established. The model includes multiple latent and actively infected stages. It is shown that the probability of a major infection is generally more likely after the virus has entered the target cell and the cell is actively infected. In some cases, the probability of a major infection is less likely if the burst size of actively infected cells is small.     

An Approximation Method for Improving Dynamic Network Model Fitting

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, that is, networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a nonnegligible computational burden, is much easier. This article examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail—networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.     

Image Restoration Using Modifications of Simulated Annealing

Abstract

This article uses a modified version of the simulated annealing algorithm to restore degraded spatial patterns. Standard simulated annealing is used to find an image that is a posterior mode when the number of images under consideration precludes sequential search for a maximum. I incorporate jumping probabilities of the annealing algorithm without randomization. The convergence of our algorithm is proven under a practical annealing schedule. The same idea is also implemented to improve the performance of other modifications of simulated annealing. These include forcing proportions of labels in an image, using posterior marginals, and incorporating an edge process. This article also studies nonlinear presmoothing of the observations.     

客户发展关系的Markov链一般模型

根据客户发展关系的Markov链的转移概率矩阵，建立了客户发展关系的一般模型，它包含许多特殊模型。前人研究的一些模型正是该一般模型的特例。一般模型的建立不但刻画了各种客户发展关系，而且为企业对客户发展进行定量分析和管理奠定了基础。     

Path coupling without contraction

Path coupling is a useful technique for simplifying the analysis of a coupling of a Markov chain. Rather than defining and analysing the coupling on every pair in Ω×Ω, where Ω is the state space of the Markov chain, analysis is done on a smaller set SΩ×Ω. If the coefficient of contraction β is strictly less than one, no further analysis is needed in order to show rapid mixing. However, if β=1 then analysis (of the variance) is still required for all pairs in Ω×Ω. In this paper we present a new approach which shows rapid mixing in the case β=1 with a further condition which only needs to be checked for pairs in S, greatly simplifying the work involved. We also present a technique applicable when β=1 and our condition is not met.     

The type problem for random walks on trees

We consider the question of whether the simple random walk (SRW) on an infinite tree is transient or recurrent. For random-trees (all vertices of distancen from the root of the tree have degreed _n , where {d _n } are independent random variables), we prove that the SRW is a.s. transient if lim inf _n n E(log(d _n-1))>1 and a.s. recurrent if lim sup _n n E(log(d _n-1))<1. For random trees in which the degrees of the vertices are independently 2 or 3, with distribution depending on the distance from the root, a partial classification of type is obtained.Research supported in part by NSF DMS 8710027.     

Ordered thinnings of point processes and random measures

This is a study of thinnings of point processes and random measures on the real line that satisfy a weak law of large numbers. The thinning procedures have dependencies based on the order of the points or masses being thinned such that the thinned process is a composition of two random measures. It is shown that the thinned process (normalized by a certain function) converges in distribution if and only if the thinning process does. This result is used to characterize the convergence of thinned processes to infinitely divisible processes, such as a compound Poisson process, when the thinning is independent and nonhomogeneous, stationary, Markovian, or regenerative. Thinning by a sequence of independent identically distributed operations is also discussed. The results here contain Renyi's classical thinning theorem and many of its extensions.     

随机环境中耦合空间的不变测度存在性

本文研究了随机环境中耦合空间上不变测度存在性问题,证明了一些存在性定理．     

The Construction of Denumerable q-Processes in Random Environments-The Existence and Uniqueness

The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.     

从p—m链到随机环境中的马氏链

第一节引进了p一m链的概念,并用之构造了与它相应的随机环境中的马氏链和绕积马氏链、第二节引进了一系列与随机环境中的马氏链相关的概率特性函数,并得到了这些函数之间的一系列关系.这些结果是经典马氏链的相应结果的一般化,它们在随机环境中的马氏链的极限理论的研究中是很有用的。     

带泊松跳跃的几何布朗运动的经济模型

本文讨论了带泊松过程的几何布朗运动的经济模型,在收益函数R(x)=ax2-b的情形下,利用伊藤公式,求得平均收益的最优解.     

绕积马氏链的中心极限定理

讨论了具有离散参数的绕积马氏链的中心极限定理,给出了加在过程样本函数上充分条件。得到了绕积马氏链的中心极限定理成立的充分条件.     

随机环境中马氏链的强常返性

讨论了随机环境中马氏链的强常返性,给出了在一类条件下,弱常返是强常返的及判定X是强常返的一个充分条件.     

A Markov Risk Model with Two Classes of Insurance Business

A Markov risk model with two classes of insurance business is studied. In this model, the two classes of insurance business are independent. Each of the two independent claim number processes is the number of jumps of a Markov jump process from time 0 to t, whichever has not independent increments in general. An integral equation satisfied by the ruin probability is obtained and the bounds for the convergence rate of the ruin probability are given by using a generalized renewal technique.     

Continuous Contour Monte Carlo for Marginal Density Estimation With an Application to a Spatial Statistical Model

The problem of marginal density estimation for a multivariate density function f(x) can be generally stated as a problem of density function estimation for a random vector λ(x) of dimension lower than that of x. In this article, we propose a technique, the so-called continuous Contour Monte Carlo (CCMC) algorithm, for solving this problem. CCMC can be viewed as a continuous version of the contour Monte Carlo (CMC) algorithm recently proposed in the literature. CCMC abandons the use of sample space partitioning and incorporates the techniques of kernel density estimation into its simulations. CCMC is more general than other marginal density estimation algorithms. First, it works for any density functions, even for those having a rugged or unbalanced energy landscape. Second, it works for any transformation λ(x) regardless of the availability of the analytical form of the inverse transformation. In this article, CCMC is applied to estimate the unknown normalizing constant function for a spatial autologistic model, and the estimate is then used in a Bayesian analysis for the spatial autologistic model in place of the true normalizing constant function. Numerical results on the U.S. cancer mortality data indicate that the Bayesian method can produce much more accurate estimates than the MPLE and MCMLE methods for the parameters of the spatial autologistic model.