Chen, Le Kim, Kunwoo
Published in
Acta Mathematica Scientia

In this article, we study the nonlinear stochastic heat equation in the spatial domain ℝd subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang’s condition. We establish the existence and uniqueness of a random field ...

Ren, Panpan Wu, Jiang-Lun
Published in
Acta Mathematica Scientia

In this article, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing ...

Hu, Yaozhong
Published in
Acta Mathematica Scientia

This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solutio...

Wang, Yuzhu Tian, Naiwen
Published in
Acta Mathematica Scientia

In this article, we focus on the Cauchy problem for the generalized IMBq system in n-dimensional space, which arises from DNA. We show the global existence and decay estimates of solution for a class of initial velocity, provided that the initial value is suitably small.

Peng, Ru Xing, Xiaolei Jiang, Liangying
Published in
Acta Mathematica Scientia

This article is devoted to characterizing the boundedness and compactness of multiplication operators from Hardy spaces to weighted Bergman spaces in the unit ball of ℂn.

Dai, Duanxu Zheng, Bentuo
Published in
Acta Mathematica Scientia

A pair of Banach spaces (X, Y) is said to be stable if for every ε-isometry f : X → Y, there exist γ > 0 and a bounded linear operator T : L(f ) → X with ‖T‖ ≤ α such that ‖Tf (x) — x‖ ≤ γε for all x ∈ X, where L(f ) is the closed linear span of f (X). In this article, we study the stability of a pair of Banach spaces (X, Y) when X is a C(K) space....

Wang, Zhonghua Yan, Qiming
Published in
Acta Mathematica Scientia

In this article, we prove a Picard-type Theorem and a uniqueness theorem for non-Archimedean analytic curves in the projective space ℙn (F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} ...

Es-Sebaiy, Khalifa Alazemi, Fares Al-Foraih, Mishari
Published in
Acta Mathematica Scientia

In this article, we consider the drift parameter estimation problem for the nonergodic Ornstein-Uhlenbeck process defined as dXt = θXtdt + dGt, t ≥ 0 with an unknown parameter θ > 0, where G is a Gaussian process. We assume that the process {Xt,t ≥ 0} is observed at discrete time instants t1 = Δn, …, tn = nΔn, and we construct two least squares typ...

Hu, Guangming Qi, Yi
Published in
Acta Mathematica Scientia

Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials are constructed in [5, 6]. The Strebel rays [3] and the eventually distance minimizing rays [9] are important in Teichmüller spaces an...

He, Yue Her, Hai-Long
Published in
Acta Mathematica Scientia

Let M be a (2k + 2l + 2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary kernels and foliations. We show the relationship between a pair of vector fields for a contact pair and a quadruple of functions on M. ...