ELEMENTARY AND Ф-FREE LIE TRIPLE SYSTEMS

We introduce elementary and Φ-free Lie triple systems and study the properties of these systems.In particular,structures of subsystems of an elementary Lie triple system and a class of Φ-free Lie triple systems are investigated.     

Change-point inference on volatility in noisy Itô semimartingales

This work is concerned with tests on structural breaks in the spot volatility process of a general Itô semimartingale based on discrete observations contaminated with i.i.d. microstructure noise. We construct a consistent test building up on infill asymptotic results for certain functionals of spectral spot volatility estimates. A weak limit theorem is established under the null hypothesis relying on extreme value theory. We prove consistency of the test and of an associated estimator for the change point. A simulation study illustrates the finite-sample performance of the method and efficiency gains compared to a skip-sampling approach.     

On σ-Embedded and σ-n-Embedded Subgroups of Finite Groups

Siberian Mathematical Journal - Let G be a finite group, and let σ = {σi | i ∈ I} be a partition of the set of all primes ℙ and σ(G) = {σi | σi ∩...     

The Isomorphisms of Symplectic Groups over Ф-surjective Rings

Let i2 and R_1 are Φ-surjective rings with 2 as a unit. Then A: S_(P_n)(R)→S_(P_(n1)),(R_1) is agroup isomorphism if and only if n=n_1, there exists a ring homomorphism σ: R→R_1 and Ahas the standard form AX=PX~σP~(-1), for all X inS_(p_n)(R), where P is a generalized symplec-tic matrix.     

Functional estimation for Lévy measures of semimartingales with Poissonian jumps

We consider semimartingales with jumps that have finite Lévy measures. The purpose of this article is to estimate integral-type functionals of the Lévy measures from discrete observations. We propose two types of estimators: kernel-type and empirical-type estimators, both of which are obtained by direct discretization from asymptotically efficient estimators of the target based on continuous observations. We show the asymptotic efficiency in the asymptotic minimax sense of our estimators as the sample size tends to infinity and the sampling interval tends to zero.     

Locally Asymptotic-norming Property and Kadec Property

In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.     

Characterization of residual σ-algebras

The behavior of residual -algebras is studied. For a probability space (, , P) a new topology is introduced on the set of all -subalgebras. Necessary and sufficient conditions for the independence of events from the final -algebra are obtained in terms of mixing.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1149–1152, August, 1992.     

On the Equivalence of the Mizoguchi-Takahashi Locally Contractive Map and the Nadler’s Locally Contractive Map

Abstract

In this paper, the equivalence between multi-valued maps satisfying the Mizoguchi-Takahashi’s uniformly locally contractive condition and multi-valued maps satisfying the Nadler’s uniformly locally contractive condition is obtained on metrically convex space. We have provided examples to illustrate that this equivalence need not be true on any arbitrary metric space.     

On Pointwise Uniform and Locally Uniform Spaces

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Itô correction terms for the radial parts of semimartingales on manifolds

Summary We consider functions,F, of a semimartingale,X, on a complete manifold which fail to beC ² only on, and are sufficiently well-behaved near, a codimension 1 subset . We obtain an extension of the Itô formula which is valid for all time by adding a continuous predictable process given explicitly in terms of two geometric local times ofX on and the Gâteaux derivative ofF. We then examine the cut locus of a point of the manifold in sufficient detail to show that this result applies to give a corresponding expression for the radial part of the semimartingale.     

The Infinite-dimensional σ-widthsof Besov Classes

Let (X(Rd), x) be a normed space of real functions on Rd. Let > 0 and P be theoperator in X(Rd) defined by P f(x) = x(x)f(x) (where (x) is the characteristic functionof the cube Id = [- , ]d). Let L be a subspace of X(Rd). Set P L= {P f: f L}. SupposeL is locally-finite dimensional, i.e., dim(P L,X) < for every > 0. Then the followingquantity is said to be the average dimension of L in X (in the sense of LED)(see [1]).Let > 0, and C be a centrally symmetric subset of X(Rd). The i…