Acta Mathematica Sinica-English Series最新文献

This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces. The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean (p ≥ 2). As an application, a classical limit theorem on the dependence of such equations on a parameter is obtained. The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.

We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ^d with d ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝ^d, their local times exist when d ≤ 3. A Tanaka formula of the local time is also derived.

In this paper, we study a family of Hartogs domains fibred over Hermitian symmetric manifolds being a unit ball in ℂ^m. The aim of the present study is to establish the rigidity results about proper holomorphic mappings between two equidimensional Hartogs domains over Hermitian symmetric manifolds. In particular, we can fully determine its biholomorphic equivalence and automorphism group.

In this paper, we consider the following perturbed fractional Hamiltonian systems

where (alpha in (1/2,1],,,L in C(mathbb{R},{mathbb{R}^{N times N}})) is symmetric and not necessarily required to be positive definite, (W in {C^1}(mathbb{R}times {mathbb{R}^N},mathbb{R})) is locally subquadratic and locally even near the origin, and perturbed term (G in {C^1}(mathbb{R} times {mathbb{R}^N},mathbb{R})) maybe has no parity in u. Utilizing the perturbed method improved by the authors, a sequence of nontrivial homoclinic solutions is obtained, which generalizes previous results.

In this paper, we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence. The Cremér-type moderate deviations, as well as the moderation deviation principle with explicit rate function can be obtained.

We completely characterize the boundedness of area operators from the Bergman spaces (A_alpha ^p({mathbb{B}_n})) to the Lebesgue spaces ({L^q}({mathbb{S}_n})) for all 0 < p,q < ∞. For the case n = 1, some partial results were previously obtained by Wu in [Wu, Z.: Volterra operator, area integral and Carleson measures, Sci. China Math., 54, 2487–2500 (2011)]. Especially, in the case q < p and q < s, we obtain some characterizations for the area operators to be bounded. We solve the cases left open there and extend the results to n-complex dimension.

In this paper we focus on the boundary regularity for a class of k-Hessian equations which can be degenerate and (or) singular on the boundary of the domain. Motivated by the case of Monge–Ampère equations, we first construct sub-solutions, then apply the characteristic of the global Hölder continuity for convex functions, and finally use the maximum principle to obtain the boundary Hölder continuity for the solutions of the k-Hessian equations. However, finding such sub-solutions is very difficult due to the complexity of the k-Hessian operator. In particular, we employ the symmetric mean to overcome the difficulties.

We establish new identities for Moore–Penrose inverses of some operator products, and prove their associated reverse-order laws. Moreover, our results concerning the Moore–Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville’s inclusions are made into equalities.

We study the following Schrödinger equation with variable exponent

where (epsilon > 0,,,1 < p < {{N + 2} over {N - 2}},,,a(x) in {C^1}({mathbb{R}^N}) cap {L^infty }({mathbb{R}^N}),,,N ge 3) Under certain assumptions on a vector field related to a(x), we use the Lyapunov–Schmidt reduction to show the existence of single peak solutions to the above problem. We also obtain local uniqueness and exact multiplicity results for this problem by the Pohozaev type identity.

Multiple change-points estimation for functional time series is studied in this paper. The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions. Group least absolute shrinkage and selection operator (LASSO) is then applied to estimate the number and the locations of possible change points. However, the group LASSO (GLASSO) always overestimate the true points. To circumvent this problem, a further Information Criterion (IC) is applied to eliminate the redundant estimated points. It is shown that the proposed two-step procedure estimates the number and the locations of the change-points consistently. Simulations and two temperature data examples are also provided to illustrate the finite sample performance of the proposed method.