Geostochastic calculus

A stochastic calculus for a family of continuous measure-valued Markov processes is developed. Such processes arise naturally in the construction of stochastic models of spatially distributed populations. The stochastic calculus is a tool whereby a class of density-dependent models can be studied in terms of the multiplicative measure diffusion process. In this paper the stochastic integral is introduced in the space-time setting and a Cameron-Martin-Girsanov theorem is established.     

美国法律过程学派对现实主义法学挑战的回应

现实主义法学的价值相对主义立场与经验主义研究方法对自兰德尔以来的古典正统体系所捍卫的自由主义法治提出了挑战。法律过程学派通过提出“制度解决的原则”,将法的合法性建立于程序之上,并以“制度能力”为基石建构其理论框架,通过对司法“理性阐述”过程的强调来彰显司法的比较优势并以此区别和协调其与立法、行政及私人秩序之间的关系,对宪法审查的“反多数难题”,则提出了“中立原则”的解决方法。二十世纪六十年代以后,法律过程学派随着美国社会基本共识的破裂而迅速衰落,但该学派的诸多理论立场在美国学界至今仍受重视。     

Large Deviations for Empirical Estimators of the Stationary Distribution of a Semi-Markov Process with Finite State Space

We prove the large deviation principle for empirical estimators of stationary distributions of semi-Markov processes with finite state space, irreducible embedded Markov chain, and finite mean sojourn time in each state. We consider on/off Gamma sojourn processes as an illustrative example, and, in particular, continuous time Markov chains with two states. In the second case, we compare the rate function in this article with the known rate function concerning another family of empirical estimators of the stationary distribution.     

A Note on the Poisson Likelihood Ratio Test Statistic for Kulldorff's Scan Methods

Methods based on scan statistics are widely used in health-related applications to detect clusters of disease. The most common methods are based on the Bernoulli and Poisson models. Kulldorff (1997 Kulldorff , M. ( 1997 ). A spatial scan statistic . Communications in Statistics—Theory and Methods 26 : 1481 – 1496 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) derived the likelihood ratio test statistic for his scan method for both of these models. His scan statistic is widely used with freely available software, SaTScan^? (see Kulldorff, 2005 Kulldorff , M. ( 2005 ). SaTScan: software for the spatial, temporal, and space-time scan statistics , version 5.1 [computer program]. Information Management Services 2005; Available: http://www.satscan.org/. Accessed July 2007 . [Google Scholar]). We provide an alternative derivation of the likelihood ratio test statistic in the Poisson case. Our derivation is simpler and more general in the sense that it applies when the incidences are not aggregated into subregional counts.     

Decomposition of Scatter Ratios Used in Monitoring Multivariate Process Variability

Wilks’ ratio statistic can be defined in terms of the ratio of the sample generalized variances of two non-independent estimators of the same covariance matrix. Recently this statistic has been proposed as a control statistic for monitoring changes in the covariance matrix of a multivariate normal process in a Phase II situation, particularly when the dimension is larger than the sample size. In this article we derive a technique for decomposing Wilks’ ratio statistic into the product of independent factors that can be associated with the components of the covariance matrix. With these results, we demonstrate that, when a signal is detected in a control procedure for the Phase II monitoring of process variability using the ratio statistic, the signaling value can be decomposed and the process variables contributing to the signal can be specifically identified.     

The Dynamic Model for Cancer Relapse Based on Two-Stage Model of Carcinogenesis

In this article, the time from the start of chemotherapy randomization until cancer relapse is of primary interest. Here, cancer relapse refers to the appearance of the first observable malignant clone after therapy. A dynamic model for cancer relapse after chemotherapy is developed. The model differs from the traditional cure rate models in that it takes into consideration the growth kinetics of malignant tumors using a two-stage carcinogenesis model. The survival and hazard functions for cancer relapse time are derived, and a simulation study is performed to validate the underlying model.     

Precise Asymptotics in Complete Moment Convergence of Parameter Estimator in the Gaussian Autoregressive Process

In this article, we study the precise asymptotic behaviors of the least-squares estimator in the Gaussian autoregressive process. Two kinds of complete moment convergence of this estimator can be obtained by the methods of deviation inequalities for this estimator and nonuniform Berry-Esseen bound for martingales.     

Semi-Markov Disability Insurance Models

In this article, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.     

A cold standby repairable system with the repairman having multiple vacations and operational,repair, and vacation times following phase-type distributions

ABSTRACT

This paper studies a cold standby repairable system with two identical components and one repairman having multiple vacations applying matrix-analytic methods. The lifetime of the component follows a phase-type distribution. The repair times and the vacation times of the repairman are governed by different phase-type distributions, respectively. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime, the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated, respectively. A numerical application is performed to illustrate the calculations.