On representations,inversions, and approximations of laplace transforms in banach spaces

The paper extend's some of the basic results of classical Laplace transform theory to the Laplace transform of bounded Bochner integrable functions and the Laplace-Stieltjes transform of Lipschitz continuous functions with values in a Banach space.     

A bayesian approach to inference for monotone failure rates

In reliability theory, the notion of monotone failure rates plays a central role. When prior information indicates that such monotonicity is meaningful, it must be incorporated into the prior distribution whenever inference about the failure rates needs to be made. In this paper we show how this can be done in a straightforward and intuitively pleasing manner. The time interval is partitioned into subintervals of equal width and the number of failures and censoring in each interval is recorded. By defining a Dirichlet as the joint prior distribution for the forward or the backward differences of the conditional probabilities of survival in each interval, we find that the monotonicity is presenved in the posterior estimate of the failure rates. A posterior estimate of the survival function can also be obtained. We illustrate our method by applying it to some real life medical data.     

条件VaR和条件CVaR的核估计及其实证分析

VaR和CVaR是目前两种主流风险度量工具。条件VaR和条件CVaR是基于市场风险因子在已知条件(或信息)下的分布来计量和测算VaR和CVaR,能够及时地根据变化的条件来重新估计风险进而进行有效的风险管理,是对传统的基于边际分布的VaR和CVaR指标的有益补充。另外一方面,近年来非参数核估计方法因模型设定灵活、方便处理变量相依结构等优点备受关注。在本文,我们用条件VaR和条件CVaR的非参数核估计法,对我国A股市场的风险进行测算。结果得出:条件VaR和条件CVaR能揭示出深证成指和上证综指之间的不同风险特征;条件VaR和条件CVaR的测算结果并非总是一致;系统风险估计值对已知条件的敏感性高于深发展A和万科A两只股票的个股风险。以上风险特征在边际VaR和边际CVaR下无法得到。     

Optimum inspection under competing risks with proportional hazards

In this work, we present an inspection policy so as to detect the failures of a single‐unit system subject to N latent causes of failure when the time and cause of failure are independent. It is supposed that inspections may fail and give an erroneous result. The optimum inspection time which minimizes cost per unit of time for an infinite time span is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Stahel-Donoho kernel estimation for fixed design nonparametric regression models

This paper reports a robust kernel estimation for fixed design nonparametric regression models. A Stahel-Donoho kernel estimation is introduced, in which the weight functions depend on both the depths of data and the distances between the design points and the estimation points. Based on a local approximation, a computational technique is given to approximate to the incomputable depths of the errors. As a result the new estimator is computationally efficient. The proposed estimator attains a high breakdown point and has perfect asymptotic behaviors such as the asymptotic normality and convergence in the mean squared error. Unlike the depth-weighted estimator for parametric regression models, this depth-weighted nonparametric estimator has a simple variance structure and then we can compare its efficiency with the original one. Some simulations show that the new method can smooth the regression estimation and achieve some desirable balances between robustness and efficiency.     

Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models

This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate nonparametrically some characteristics of this conditional distribution. Kernel type estimators for the conditional cumulative distribution function and the successive derivatives of the conditional density are introduced. Asymptotic properties are stated for each of these estimates, and they are applied to the estimations of the conditional mode and conditional quantiles. Our asymptotic results highlightes the importance of the concentration properties on small balls of the probability measure of the underlying functional variable. So, a special section is devoted to show how our results behave in several situations when the functional variable is a continuous time process, with special attention to diffusion processes and Gaussian processes. Even if the main purpose of our paper is theoretical, an application to some chemiometrical data set coming from food industry is presented in a short final section. This example illustrates the easy implementation of our method as well as its good behaviour for finite sample sizes.     

Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions

We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)_t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,

     

Conditional stability estimation for an inverse boundary problem with non-smooth boundary in

In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in by a solution to a Cauchy problem of the Laplace equation. Assuming that the unknown part is a Lipschitz continuous surface, we give a logarithmic conditional stability estimate in determining the part of boundary under reasonably a priori information of an unknown part. The keys are the complex extension and estimates for a harmonic measure.

     

Numerical inversion of laplace transform via wavelet in partial differential equations

This article presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that P is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulae of listing table (Chen et al., Journal of The Franklin Institute 303 (1977), 267–284) to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task. The operational method presented in this article owns the advantages of simpler computation as well as broad application. We still can obtain satisfying solution even under large matrix. Moreover, we do not have numerically unstable problems. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 536–549, 2014     

Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems

We describe a bootstrap method for estimating mean squared error and smoothing parameter in nonparametric problems. The method involves using a resample of smaller size than the original sample. There are many applications, which are illustrated using the special cases of nonparametric density estimation, nonparametric regression, and tail parameter estimation.     

High‐order compact finite difference and laplace transform method for the solution of time‐fractional heat equations with dirchlet and neumann boundary conditions

The work presents a novel coupling of the Laplace Transform and the compact fourth‐order finite‐difference discretization scheme for the efficient and accurate solution of linear time‐fractional nonhomogeneous diffusion equations subject to both Dirichlet and Neumann boundary conditions. A translational transformation of the dependent variable ensures the Caputo derivative is aligned with the Riemann‐Louiville fractional derivative. The resulting scheme is computationally efficient and shown to be uniquely solvable in all cases, accurate and convergent to in the spatial domain. The convergence rates in the temporal domain are contour dependent but exhibit geometric convergence. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1184–1199, 2016     

A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory

A novel optimal preventive maintenance policy for a cold standby system consisting of two components and a repairman is described herein. The repairman is to be responsible for repairing either failed component and maintaining the working components under certain guidelines. To model the operational process of the system, some reasonable assumptions are made and all times involved in the assumptions are considered to be arbitrary and independent. Under these assumptions, all system states and transition probabilities between them are analyzed based on a semi-Markov theory and a regenerative point technique. Markov renewal equations are constructed with the convolution of the cumulative distribution function of system time in each state and corresponding transition probability. By using the Laplace transform to solve these equations, the mean time from the initial state to system failure is derived. The optimal preventive maintenance policy that will provide the optimal preventive maintenance cycle is identified by maximizing the mean time from the initial state to system failure, and is determined in the form of a theorem. Finally, a numerical example and simulation experiments are shown which validated the effectiveness of the policy.     

A nonparametric procedure to detect periods in time series

Suppose that for a given time series the experimenter knows that it has a certain periodic property and that he wishes to find out the length of the period. For this problem a nonparametric procedure is proposed. It consists of a new smoothing technique based on Kendall's Tau and a specific counting method. The procedure is studied under a simple model of periodic time series which are composed of periodic (deterministic) functions, a linear trend and exchangeable (stochastic) sequences. The performance of the procedure is illustrated by a simple example.     

Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

The finite analytic numerical method for 3D quasi‐Laplace equation with conductivity in full tensor form is constructed in this article. For cubic grid system, the gradient of the potential variable will diverge when tending to the common edge joining the four grids with different conductivities. However, the potential gradient along the tangential direction is of limited value. As a consequence, the 3D quasi‐Laplace equations will behave as a quasi‐2D one. An approximate analytical solution of the 3D quasi‐Laplace equation can be found around the common edge, which is expressed as a combination of a power‐law function and a linear function. With the help of this approximate analytical solution, a 3D finite analytical numerical scheme is then constructed. Numerical examples show that the proposed numerical scheme can provide rather accurate solutions only with or subdivisions. More important, the convergent speed of the numerical scheme is independent of the conductivity heterogeneity. In contrast, when using the traditional numerical schemes, typically such as the MPFA method, the refinement ratio for the grid cell needs to increase dramatically to get an accurate result for the strong heterogeneous case.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1475–1492, 2017     

Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models

We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent (WOD) random variables, which improve and extend the corresponding results of Y. F. Wu, M. G. Zhai, and J. Y. Peng [J. Math. Inequal., 2019, 13(1): 251–260]. As an application of the main results, we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.     

A Laplace transform method for order statistics from nonidentical random variables and its application in Phase-type distribution

In this paper, we derive a method for obtaining the Laplace transform of order statistics (o.s.) arising from general independent nonidentically distributed random variables (r.v.’s). A survey of the most important properties, applications and the o.s. of a Phase-type (PH) distribution are also presented. Two illustrative examples are provided.     

Geometric Ergodicity of Metropolis-Hastings Algorithms for Conditional Simulation in Generalized Linear Mixed Models

Conditional simulation is useful in connection with inference and prediction for a generalized linear mixed model. We consider random walk Metropolis and Langevin-Hastings algorithms for simulating the random effects given the observed data, when the joint distribution of the unobserved random effects is multivariate Gaussian. In particular we study the desirable property of geometric ergodicity, which ensures the validity of central limit theorems for Monte Carlo estimates.     

Asymptotic analysis via Mellin transforms for small deviations in L 2-norm of integrated Brownian sheets

We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared L²-norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates.Research supported by NSF grant DMS–0104167, and by The Johns Hopkins Universitys Acheson J. Duncan Fund for the Advancement of Research in Statistics.Mathematics Subject Classification (2000):Primary 60G15, 41A60; secondary 60E10, 44A15, 41A27     

Bayesian inference for Pr (Y

《Applied Mathematical Modelling》2014,38(5-6):1698-1709

Weighted Lp‐theory for vector potential operators in three‐dimensional exterior domains

In the present paper, we study the vector potential problem in exterior domains of . Our approach is based on the use of weighted spaces in order to describe the behavior of functions at infinity. As a first step of the investigation, we prove important results on the Laplace equation in exterior domains with Dirichlet or Neumann boundary conditions. As a consequence of the obtained results on the vector potential problem, we establish useful results on weighted Sobolev inequalities and Helmholtz decompositions of weighted spaces. Copyright © 2015 John Wiley & Sons, Ltd.