Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs

In this paper we consider the problem of estimating a coefficient of a strongly elliptic partial differential operator in stochastic parabolic equations. The coefficient is a bounded function of time. We compute the maximum likelihood estimate of the function on an approximating space (sieve) using a finite number of the spatial Fourier coefficients of the solution and establish conditions that guarantee consistency and asymptotic normality of the resulting estimate as the number of the coefficients increases. The equation is assumed diagonalizable in the sense that all the operators have a common system of eigenfunctions.     

高阶混合型周期系统的周期解

应用Ｆｏｕｒｉｅｒ分析的方法,结合一些不等式技巧得到了ｎ阶常系数带有滞后与超前偏差变元的混合型线性周期系统存在周期解的充要条件．     

一阶非线性常微分方程可积类型的推广

文中提出新的四类非线性常微分方程,借助某些方法与技巧,论证了这几类方程可用积分法求解,获得的结论推广了文献中相应的结果。     

Public Debt Sustainability in Africa: Building Resilience and Challenges Ahead

The increased access of African countries to international capital markets has put public debt sustainability at the forefront of the continent's policy agenda. Utilising the ‘stabilising primary‐balance’ approach, this article finds that the actual primary balances exceeded those required to keep public debt at the 2007 level in about half the countries studied, and in several cases, those needed to reduce public debt‐to‐GDP to sustainable thresholds. The interest rate‐growth differential (IRGD) drove sustainability, underscoring the importance of growth and borrowing for growth‐enhancing outlays. As the IRGDs are likely to narrow over the longer term, fiscal policies will need to play a greater role.     

Nonshared Environment Research

SUMMARY

This review focuses on conceptualizations of nonshared environment and on four areas of research that should be targeted for future growth. It is argued that there are at least two different approaches to the study of nonshared environment. “Experience-oriented” researchers center on sibling differential experiences in the family and their role in children's development. “Outcome-oriented” investigators focus on the search for environmental origins of individual differences in outcomes. Turkheimer and Waldron's (2000) concept of objective versus effective nonshared environment and Reiss and colleagues' (2000) notion of single-system versus multi-system nonshared environment processes are also discussed. Four topics for future research are outlined: (1) age-related changes and development; (2) the role of the self; (3) the role of context; and (4) the importance of extrafamilial experiences. More work in these areas will lead to useful theories of how nonshared environment processes are linked to sibling and individual differences in behavioral development and adjustment.     

Bayesian penalized B-spline estimation approach for epidemic models

Ordinary differential equations (ODEs) are normally used to model dynamic processes in applied sciences such as biology, engineering, physics, and many other areas. In these models, the parameters are usually unknown, and thus they are often specified artificially or empirically. Alternatively, a feasible method is to estimate the parameters based on observed data. In this study, we propose a Bayesian penalized B-spline approach to estimate the parameters and initial values for ODEs used in epidemiology. We evaluated the efficiency of the proposed method based on simulations using the Markov chain Monte Carlo algorithm for the Kermack–McKendrick model. The proposed approach is also illustrated based on a real application to the transmission dynamics of hepatitis C virus in mainland China.     

Generalized polya eggenberger family of distributions and its relation to lagrangian katz family

Janardan (1973) introduced the generalized Polya Eggenberger family of distributions (GPED) as a limiting distribution of the generalized Markov-Polya distribution (GMPD). Janardan and Rao (1982) gave a number of characterizing properties of the generalized Markov-Polya and generalized Polya Eggenberger distributions. Here, the GPED family characterized by four parameters, is formally defined and studied. The probability generating function, its moments, and certain recurrence relations with the moments are provided. The Lagrangian Katz family of distributions (Consul and Famoye (1996)) is shown to be a sub-class of the family of GPED (or GPED ₁ ) as it is called in this paper). A generalized Polya Eggenberger distribution of the second kind (GPED ₂ ) is also introduced and some of it's properties are given. Recurrence relations for the probabilities of GPED ₁ and GPED ₂ are given. A number of other structural and characteristic properties of the GPED ₁ are provided, from which the properties of Lagrangian Katz family follow. The parameters of GMPD ₁ are estimated by the method of moments and the maximum likelihood method. An application is provided.     

Anticipated Backward Stochastic Differential Equation with Reflection

In this article, we deal with anticipated backward stochastic differential equation with reflecting boundary. The existence and uniqueness of solution is obtained for equation with Lipschitz and non-Lipschitz generator.     

关于新型期权及其定价模型的研究

本文剖析了新型期权的生成机理和主要特征,由此归纳出新型斯权的主要类型.在标准期权定价模型的基础上,深入讨论了各类新型期权的定价模型,并重点研究了路径依赖型期权的定价问题,创建了包含路径因子在内的定价模型,最后对多因素新型期权的定价进行了展望.     

Statistical analysis of error for fourth-order ordinary differential equation solvers

We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams–Bashforth method and a new method that randomly switches between the Milne and Adams–Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.