The Finite-time Ruin Probability for the Jump-Diffusion Model with Constant Interest Force

In this paper, we consider the finite time ruin probability for the jump-diffusion Poisson process. Under the assurnptions that the claimsizes are subexponentially distributed and that the interest force is constant, we obtain an asymptotic formula for the finite-time ruin probability. The results we obtain extends the corresponding results of Kliippelberg and Stadtmüller and Tang.     

Gaining efficiency via weighted estimators for multivariate failure time data

Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator. We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed using the proposed estimators. This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10 ^th five year plan of 211 Project for Shanghai University of Finance and Economics (the 3 ^rd phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444)     

Modified likelihood ratio test for homogeneity in bivariate normal mixtures with presence of a structural parameter

This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution.     

Ruin probabilities in the risk process with random income

We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.     

Ruin Probabilities of a Surplus Process Described by PDMPs

In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process （PDMP）. An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen, the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed.     

A new proof of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the parabolic polyharmonic equations

In this paper we obtain local L ^p estimates for the parabolic polyharmonic equations by a straightforward approach. Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)     

The Gaussian approximation for multi-color generalized Friedman’s urn model

The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of ...     

Minimal circumscribed Hermitian ellipsoid of Hartogs domains and an application to an extremal problem

In this paper we construct circumscribed Hermitian ellipsoids of Hartogs domains of least volume and as an application, we obtain the Carath′eodory extremal mappings between the Hartogs domains and the unit ball, and also give an explicit formula for calculating the extremal values.     

Consistency and asymptotic normality of profilekernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models

Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies. This work was supported by National Natural Science Foundation of China (Grant Nos. 10561008, 10761011), Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. Y200805073), PhD Special Scientific Research Foundation of Chinese University (Grant No. 20060673002) and Program for New Century Excellent Talents in University (Grant No. NCET-07-0737)     

Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.     

The Paley-Wiener theorem in the non-commutative and non-associative octonions

The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved. This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002)     

An overview of representation theorems for static risk measures

In this paper, we give an overview of representation theorems for various static risk measures: coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders. This work was supported by National Natural Science Foundation of China (Grant No. 10571167), National Basic Research Program of China (973 Program) (Grant No. 2007CB814902), and Science Fund for Creative Research Groups (Grant No. 10721101)     

Asymptotic expansions for the distribution functions of Pickands-type estimators

The asymptotic expansions for the distribution functions of Pickands-type estimators in extreme statistics are obtained. In addition, several useful results on regular variation and intermediate order statistics are presented. Project supported by the National Natural Science Foundation of China (Grant No. 19601007) and Doctoral Program Foundation of Higher Education of China.     

On the error term in Weyl’s law for the Heisenberg manifolds (II)

In this paper we study the mean square of the error term in the Weyl’s law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established. This work was supported by National Natural Science Foundation of China (Grant No. 10771127)     

Global solutions of stochastic 2D Navier-Stokes equations with Lévy noise

In this paper, we prove the global existence and uniqueness of the strong and weak solutions for 2D Navier-Stokes equations on the torus perturbed by a Lévy process. The existence of invariant measure of the solutions are proved also. This work was supported by National Basic Research Program of China (Grant No. 2006CB8059000), Science Fund for Creative Research Groups (Grant No. 10721101), National Natural Science Foundation of China (Grant Nos. 10671197, 10671168), Science Foundation of Jiangsu Province (Grant Nos. BK2006032, 06-A-038, 07-333) and Key Lab of Random Complex Structures and Data Science, Chinese Academy of Sciences     

Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ

Some results on convergence of Newton‘s method in Banach spaces are established under the assumption that the derivative of the opderators satisfies the radius or center Lipschitz condition with a weak L average.     

Local structure-preserving algorithms for partial differential equations

In this paper, we discuss the concept of local structure-preserving algorithms (SPAs) for partial differential equations, which are the natural generalization of the corresponding global SPAs. Local SPAs for the problems with proper boundary conditions are global SPAs, but the inverse is not necessarily valid. The concept of the local SPAs can explain the difference between different SPAs and provide a basic theory for analyzing and constructing high performance SPAs. Furthermore, it enlarges the applicable scopes of SPAs. We also discuss the application and the construction of local SPAs and derive several new SPAs for the nonlinear Klein-Gordon equation. This work was supported by the National Basic Research Program (Grant No. 2005CB321703). The first author was supported by the National Natural Science Foundation of China (Grant Nos. 40405019, 10471067) and the Major Research Projects of Jiangsu Province (Grant No. BK2006725); the second author was supported by the National Natural Science Foundation of China (Innovation Group) (Grant No. 40221503) and the third author was supported by the National Natural Science Foundation of China (Grant No. 10471145)     

The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices

In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated. Supported by National Natural Science Foundation of China (No. 10531070), National Basic Research Program of China 973 Program (No. 2006CB805900), National Research Program of China 863 Program (No. 2006AA11Z209) and the Natural Science Foundation of Shanghai (Grant No. 06ZR14049).     

The structure of zero-divisor semigroups with graph K n ○K 2

This paper determines all commutative zero divisor semigroups whose zero divisor graph is a complete graph (finite or infinite), or a complete graph (finite or infinite) with one additional end vertex, and gives formulas for the numbers of all such semigroups with n elements. The research of T. Wu is supported by the National Natural Science Foundation of China (Grant No. 10671122) and the Natural Science Foundation of Shanghai (Grant No. 06ZR14049).     

2-Cocycles of original deformative Schr?dinger-Virasoro algebras

Both original and twisted Schr?dinger-Virasoro algebras, and also their deformations were introduced and investigated in a series of papers by Henkel, Roger and Unterberger. In the present paper we aim at determining the 2-cocycles of original deformative Schr?dinger-Virasoro algebras. This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471091, 10671027), Foundation of Shanghai Education Committee (Grant No. 06FZ029) and “One Hundred Talents Program” from University of Science and Technology of China