数学物理学报(英文版)

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PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

龙红卫

数学物理学报(英文版). 2010 (3): 645-663. DOI: 10.1016/S0252-9602(10)60067-7

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We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small α-stable noises, observed at n regularly spaced time points t_i=i/n, i=1, …, n on [0,1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator(LSE) when a small dispersion parameter ε→0 and n → ∝simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

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THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS

吕玉华, 吴荣, 徐润

数学物理学报(英文版). 2010 (3): 664-676. DOI: 10.1016/S0252-9602(10)60068-9

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In this article, the joint distributions of several actuarial diagnostics which are important to insurers' running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Lévy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.

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ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

田萍, 杨林, 薛留根

数学物理学报(英文版). 2010 (3): 677-687. DOI: 10.1016/S0252-9602(10)60069-0

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In this article, a partially linear single-index model for longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.

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UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE

明瑞星, 何晓霞, 胡亦钧, 刘娟

数学物理学报(英文版). 2010 (3): 688-700. DOI: 10.1016/S0252-9602(10)60070-7

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We consider a discrete time risk model in which the net payout (insurance risk){X_k,, k=1,2, …} are assumed to take real values and belong to the heavy-tailed class L ∩ D and the discount factors (financial risk) {Y_k, k=1, 2, …} concentrate on [θ, L], where 0<θ<1, L<∞, {X_k, k=1, 2, …}, and {Y_k, k=1, 2, …} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n≥1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278--1299).

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LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS

夏红强

数学物理学报(英文版). 2010 (3): 701-712. DOI: 10.1016/S0252-9602(10)60071-9

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We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit
theorem holds, and the speed in the central limit theorem is O(1√n}).

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EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS

曾宪忠, 刘振海

数学物理学报(英文版). 2010 (3): 713-725. DOI: 10.1016/S0252-9602(10)60072-0

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This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that p_c= (σ+m)n(n-σ-2) is its critical exponent provided {-1, [(1-m)n-2](n+1)} < σ < n-2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Furthermore, we demonstrate that if max{1, σ + m} < p ≤ p_c, then every positive solution of the equations blows up in finite time; whereas for p < p_c, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n ≤ σ + 2.

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QUASILINEAR-ADDITIVE PROPERTIES AND APPLICATIONS

张孝惠, 王根娣, 褚玉明

数学物理学报(英文版). 2010 (3): 726-732. DOI: 10.1016/S0252-9602(10)60073-2

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In this article, the authors study some basic properties of the so-called quasilinear-additive functions, and some
applications to the special functions of quasiconformal analysis are specified.

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THE CONSISTENCY AND ASYMPTOTIC NORMALITY OF NEAREST NEIGHBOR DENSITY ESTIMATOR UNDER α- |MIXING CONDITION

刘妍岩, 张艳丽

数学物理学报(英文版). 2010 (3): 733-738. DOI: 10.1016/S0252-9602(10)60074-4

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We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.

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THE DUAL BRUNN-MINKOWSKI INEQUALITIES FOR STAR DUAL OF MIXED INTERSECTION BODIES

朱先阳, 沈亚军

数学物理学报(英文版). 2010 (3): 739-746. DOI: 10.1016/S0252-9602(10)60075-6

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In this article, some dual Brunn-Minkowski inequalities are established for star dual of mixed intersection
bodies with respect to the harmonic p-combination and p-radial linear combination.

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SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS |IN COMPLEX CLIFFORD ANALYSIS

库敏, 杜金元, 王道顺

数学物理学报(英文版). 2010 (3): 747-768. DOI: 10.1016/S0252-9602(10)60076-8

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In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cⁿ⁺¹, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D?^mf=0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cⁿ⁺¹, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.

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CONTACT PROCESS ON HEXAGONAL LATTICE

姚强, 李群昌

数学物理学报(英文版). 2010 (3): 769-790. DOI: 10.1016/S0252-9602(10)60077-X

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In this article, we discuss several properties of the basic contact process on hexagonal lattice ${\Bbb H}$, showing that it behaves quite similar to the process on d-dimensional lattice Z^d in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

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OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER

袁海丽, 胡亦钧

数学物理学报(英文版). 2010 (3): 791-798. DOI: 10.1016/S0252-9602(10)60078-1

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In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant
barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.

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STRONG SOLUTIONS FOR THE INCOMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE

谭忠, 王焰金

数学物理学报(英文版). 2010 (3): 799-809. DOI: 10.1016/S0252-9602(10)60079-3

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In this article, we are concerned with the strong solutions for the incompressible fluid models of Korteweg type in a bounded domain Ω ( R³. We prove the existence and uniqueness of local strong solutions to the initial boundary value problem. We point out that in this article we allow the existence of initial vacuum provided initial data satisfy a compatibility condition.

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THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

周惊雷, 李庆国

数学物理学报(英文版). 2010 (3): 810-818. DOI: 10.1016/S0252-9602(10)60080-X

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Let (L, ≤, ∨, ∧) be a complete Heyting algebra. In this article, the linear system Ax=b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by ∨ and ∧ respectively, is studied. We obtain: (i) the necessary and sufficient conditions for S(A, b)≠Ø; (ii) the necessary conditions for |S(A, b)| =1. We also obtain the vector x ∈ L_n and prove that it is the largest
element of S(A, b) if S(A, b)≠Ø.

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MANIFOLDS WITH POINTWISE PINCHED RICCI CURVATURE

顾会玲

数学物理学报(英文版). 2010 (3): 819-829. DOI: 10.1016/S0252-9602(10)60081-1

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In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.

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INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N

贺小明, 邹文明

数学物理学报(英文版). 2010 (3): 830-840. DOI: 10.1016/S0252-9602(10)60082-3

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In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents
-?u-u u/|x|²=α |u|^2*(s)-2u/|x|^s+ βa(x)|u|^r-2 u, x ∈ R^N.
By means of the concentration-compactness principle and minimax methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α, β.

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A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS

刘创业

数学物理学报(英文版). 2010 (3): 841-856. DOI: 10.1016/S0252-9602(10)60083-5

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In this article, we consider the dynamics of N two-dimensional boson systems interacting through a pair potential N^-1V_a(x_i-x_j) where V_a(x)=a^-2V(x/a). It is well known that the Gross-Pitaevskii (GP) equation is a nonlinear Schrodinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if u_tsolves the GP equation, then the family of k-particle density matrices { _ku_t, k ≥1} solves the GP hierarchy. Denote by ψ_{N, t} the solution to the N-particle Schr\"odinger equation. Under the assumption that a =N^-ε for 0< ε<3/4, we prove that as N → ∞ the limit points of the k-particle density matrices of ψ^{_{N, t}}are solutions of the GP hierarchy with the coupling constant in the
nonlinear term of the GP equation given by ∫V(x)dx.

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POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

陈振龙, 李慧琼

数学物理学报(英文版). 2010 (3): 857-872. DOI: 10.1016/S0252-9602(10)60084-7

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Let B^{H, K}=B^{H, K}(t), t ∈ R^N₊} be an (N, d)-bifractional Brownian sheet with Hurst indices H=(H₁,…, H_N) ∈ (0, 1)^N and K=(K₁, …, K_N) ∈ (0, 1]^N. The properties of the polar sets of B^{H, K}are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^{H, K} are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

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NATURAL FROBENIUS SUBMANIFOLDS

林洁珠

数学物理学报(英文版). 2010 (3): 873-889. DOI: 10.1016/S0252-9602(10)60085-9

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I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This article will give a necessary and sufficient condition and classify the natural Frobenius hypersurfaces.

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RIGIDITY THEOREMS OF CLIFFORD TORUS

张运涛

数学物理学报(英文版). 2010 (3): 890-896. DOI: 10.1016/S0252-9602(10)60086-0

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In this article, we prove that the Clifford torus S¹(√1-r²) ×Sⁿ^-1(r) is the only closed hypersurface in the unit sphere Sⁿ⁺¹(1) with infinite fundamental group, which satisfy r²≥(n-1)/n, Ric_M ≤ C_-(H), and S ≤ S₊(H). Moreover, we give a characterization of Clifford torus S¹(√1-r²) ×Sⁿ^-1(r) with r² ={2(n-1)+nH²±|H|√n²H²+4(n-1)/2n(1+H²}.

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COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS

默会霞

数学物理学报(英文版). 2010 (3): 897-906. DOI: 10.1016/S0252-9602(10)60087-2

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Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article extends some known results.

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DISPERSION COMPARISONS OF TWO PROBABILITY VECTORS UNDER MULTINOMIAL SAMPLING

熊世峰, 李国英

数学物理学报(英文版). 2010 (3): 907-918. DOI: 10.1016/S0252-9602(10)60088-4

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We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majorization. A new dispersion index is proposed for testing the hypotheses. The corresponding test for the one-sample problem is an exact test. For the two-sample problem, the bootstrap is used to approximate the null distribution of the test statistic and the p-value. We prove that the bootstrap test is asymptotically correct and
consistent. Simulation studies for the bootstrap test are reported and a real life example is presented.

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CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

王姗姗, 张春生, 吴荣

数学物理学报(英文版). 2010 (3): 919-931. DOI: 10.1016/S0252-9602(10)60089-6

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In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.

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THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS

高凌云

数学物理学报(英文版). 2010 (3): 932-938. DOI: 10.1016/S0252-9602(10)60090-2

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We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend
some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.

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UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER

黄广月, 陈文艺

数学物理学报(英文版). 2010 (3): 939-948. DOI: 10.1016/S0252-9602(10)60091-4

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Let Ω be a connected bounded domain in Rⁿ. Denote by λ_i the i-th eigenvalue of the Laplacian operator with any order p:

{(-?)^p u=λu in Ω,
u=∂u /∂n =…=∂^p-1u / ∂n ^p^-1=0 on ∂Ω.
In this article, we give some expressions for upper bound of the (k+1)-th eigenvalue λ_k+1 in terms of the first k eigenvalues.

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VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION

温焕尧, 丁时进

数学物理学报(英文版). 2010 (3): 949-962. DOI: 10.1016/S0252-9602(10)60092-6

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In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Ginzburg-Landau equation in a smooth bounded domain $\Omega\subset{\bf R}^2$, that is, $ {\partial_tu_\varepsilon=\sum\limits_{j,k=1}^2(a_{jk}\partial_{x_k}u_\varepsilon)_{x_j}+\frac{b(x)(1-| u_\varepsilon| ^2)u_\varepsilon}{\varepsilon^2},x\in\Omega}$, and conclude that each vortex $ {b_j(t)~(j=1,2,\cdots ,N)}$ satisfies $ \frac{{\rm d}b_j(t)}{{\rm d}t}=-\big(\frac{a_{1k}(b_j(t))\partial_{x_k}a(b_j(t))}{a(b_j(t))},$ $ \frac{a_{2k}(b_j(t))\partial_{x_k}a(b_j(t))}{a(b_j(t))}\big),$ where $ {a(x)=\sqrt{a_{11}a_{22}-a_{12}^2}}$. We prove that all the vortices are pinned together to the critical points of $a(x)$. Furthermore, we prove that these critical points can not be the maximum points.

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A REMARK ON THE REGULARITY OF VECTOR-VALUED MAPPINGS DEPENDING ON TWO VARIABLES WHICH MINIMIZE SPLITTING-TYPE VARIATIONAL INTEGRALS

M. Bildhauer, M. Fuchs

数学物理学报(英文版). 2010 (3): 963-967. DOI: 10.1016/S0252-9602(10)60093-8

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We combine the maximum principle for vector-valued mappings established by D'Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u: Ω→R^N of splitting-type variational integrals provided Ω is a domain in R².

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LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

王路生, 尹景学, 王泽佳

数学物理学报(英文版). 2010 (3): 968-974. DOI: 10.1016/S0252-9602(10)60094-X

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This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration
equations

|x|^λ+k ∂u / ∂t =div(|x|^k\nabla u^m)+|x|^λ+ku^p

with 0<m<1, p>1, λ ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k_∞ and k₁ for the exponent k, such that the critical Fujita exponent p_c for p exists and is finite if k ∈ (k_∞, k₁), otherwise, p_c is infinite or does not exist.

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CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM

胡耀忠, 汪宝彬

数学物理学报(英文版). 2010 (3): 975-992. DOI: 10.1016/S0252-9602(10)60095-1

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In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral S_p(f) of fractional Brownian motion of Hurst parameter H<1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.

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THREE-SPHERE INEQUALITIES FOR SECOND ORDER SINGULAR PARTIAL DIFFERENTIAL EQUATIONS

张松艳

数学物理学报(英文版). 2010 (3): 993-1003. DOI: 10.1016/S0252-9602(10)60096-3

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In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div(A\nabla u)-Vu=0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation ∂_tu-div(A\nabla u)+Vu=0, where the singular potential V belonging to the Kato-Fefferman-Phong's class. Some applications are also discussed.

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ON SETS OF ZEROES OF CLIFFORD ALGEBRA-VALUED POLYNOMIALS

杨燕, 钱涛

数学物理学报(英文版). 2010 (3): 1004-1012. DOI: 10.1016/S0252-9602(10)60097-5

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In this note, we study zeroes of Clifford algebra-valued polynomials. We prove that if such a polynomial has only real coefficients, then it has two types of zeroes: the real isolated zeroes and the spherical conjugate ones. The total number of zeroes does not exceed the degree of the polynomial. We also present a technique for computing the zeroes.

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COMPOSITION OPERATORS FROM p-BLOCH SPACES TO LITTLE q-BLOCH SPACES |ON THE UNIT BALL OF Cⁿ

李俊锋

数学物理学报(英文版). 2010 (3): 1013-1020. DOI: 10.1016/S0252-9602(10)60098-7

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For all 0<p, q<∞, let C_φ denote the composition operator from q-Bloch spaces β^p to little p-Bloch spaces β₀^q on the unit ball of Cⁿ. In this article, necessary and sufficient conditions for C_φ to be a bounded or compact operator are given.

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