ISSN 1439-8516 CN 11-2039/O1
We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu[Stoch. Models, 31, 433-451 (2015)]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.
By assigning to each complex over a semi-simple ring two acyclicizations, we construct an explicit recollement for homotopy categories of a certain triangular matrix ring such that all the six triangle functors of the recollement preserve acyclic complexes.
This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.
For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L2(Rd), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.
In this paper, we classify the set of Lorentzian metrics on T2, analyse the topological structure of some subclasses and study whether a subclass could admit certain weak solutions to the eikonal equations.
In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space S1m+1 with parallel para-Blaschke tensors.
This paper is devoted to investigating the weighted Lp-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type (p, p) estimates for 1 < p < ∞ and the weighted weak type (1, 1) estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain Hörmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini's conditions as model examples. Meanwhile, we also obtain the weighted Lp-boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO(Rd)-functions.
In this note, first, we show that the asymptotic subcone, the ultralimit, the completion of an asymptotically PT-1 space are still an asymptotically PT-1 space. Secondly, we consider two kinds of metric spaces, which have been considered by Ibragimov and Gromov, respectively. We show that they are asymptotically PT-1 spaces under particular conditions, which provide some concrete examples of asymptotically PT-1 spaces.
In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.
