On Jackson's Inequality for Generalized Moduli of Continuity

Mathematical Notes -     

关于分数稳定过程分数参数的注

注意到分数稳定过程的样本性质和分布特征都密切关联于其分数参数,本文进一步刻画分数稳定过程关于分数参数的正则性及其对过程协差的影响.     

One Inequality for the Moduli of Continuity of Fractional Order Generated by Semigroups of Operators

Ukrainian Mathematical Journal - A new inequality for the moduli of continuity of fractional order generated by semigroups of operators is obtained. This inequality yields a generalization to the...     

On Some Properties of Multiple Moduli of Continuity

For functions of several variables a property is established similar to the well-known result of S. B. Stechkin about the metric property of almost increasing functions. In the case of one variable the proof is easier than the known one.     

大偏差与l~p-值Wiener过程在Hlder范数下的泛函连续模

本文在Holder范数生成的强拓扑下,建立了l~2-值Wiener过程的大偏差公式,从而得到了l~2-值与l~p-值Wiener过程在Holder范数下的泛函连续模.     

大偏差与lp-值Wiener过程在H(o)lder范数下的泛函连续模

本文在Holder范数生成的强拓扑下,建立了l~2-值Wiener过程的大偏差公式,从而得到了l~2-值与l~p-值Wiener过程在Holder范数下的泛函连续模.     

On Fractional Brownian Processes

We use Liouville spaces in order to prove the existence of some different fractional -Brownian motion ( 0 < 1 ), or fractional ( , )-Brownian sheets. There are also applications to the Wiener stochastic integral with respect to these -Brownian.     

Hausdorff Measures and Capacities for Increase Times of Stable Processes

Let X be a real-valued stable process. It is known that X possesses increase times iff (X ₁ > 0) > ([1]). In that case, we specify the exact Hausdorff function of the set of increase times, and characterize the subsets of [0,+) which contain increase times in terms of their capacity.     

Moduli of Continuity for Viscosity Solutions on Manifolds

We establish the estimates of modulus of continuity for viscosity solutions of nonlinear evolution equations on manifolds, extending previous work of Andrews and Clutterbuck for regular solutions on manifolds (Andrews and Clutterbuck in Anal PDE 6(5):1013–1024, 2013) and the first author’s recent work for viscosity solutions in Euclidean spaces (Li in Proc Am Math Soc 144(4):1717–1724, 2016).     

Regularity of Intersection Local Times of Fractional Brownian Motions

Let \(B^{\alpha_{i}}\) be an (N _i ,d)-fractional Brownian motion with Hurst index α _i (i=1,2), and let \(B^{\alpha_{1}}\) and \(B^{\alpha_{2}}\) be independent. We prove that, if \(\frac{N_{1}}{\alpha_{1}}+\frac{N_{2}}{\alpha_{2}}>d\), then the intersection local times of \(B^{\alpha_{1}}\) and \(B^{\alpha_{2}}\) exist, and have a continuous version. We also establish Hölder conditions for the intersection local times and determine the Hausdorff and packing dimensions of the sets of intersection times and intersection points.One of the main motivations of this paper is from the results of Nualart and Ortiz-Latorre (J. Theor. Probab. 20:759–767, 2007), where the existence of the intersection local times of two independent (1,d)-fractional Brownian motions with the same Hurst index was studied by using a different method. Our results show that anisotropy brings subtle differences into the analytic properties of the intersection local times as well as rich geometric structures into the sets of intersection times and intersection points.     

Optimal Estimates with Moduli of Continuity

In this paper we obtain estimates with optimal constants for the pointwise approximation of functions by linear positive functional, with the aid of a new second order modulus with a parameter, as well as with the aid of the first order modulus of the derivatives of functions.     

Moduli of Stable Surfaces

This article is a survey of basic facts about the moduli spaces of stable surfaces. These spaces are projective compactifications of the moduli spaces of minimal surfaces of general type. They share few of the nice features of the moduli spaces of stable curves. Some of the main pathologies are presented with some historical remarks and some more recent results on the boundary of these spaces.Received: February, 2004     

Inequalities for Moduli of Continuity in Abstract Banach Spaces

Suppose that X is a Banach space, K denotes the set of real numbers R or the set of nonnegative real numbers R _{+}, is a family of linear operators from X into X such that T _0=I is the identity operator in X, for all , and there exists M such that for all . The expression is called the rth order modulus of continuity of an element x with step h in the space X with respect to the family A(K). The properties of are studied. Bibliography: 3 titles.     

关于分数Wiener过程的不可微连续

在本文中，我们推广了Csoego＂和Shao(1994)的结果，给出了阶α（0＜α＜1）的分数Wiener过程的不可微连续模。     

On First Hitting Times for Skew CIR Processes

In this work, the first hitting times for skew CIR processes are investigated. We compute the Laplace transforms and the means of the first hitting times of some given levels. The solutions for Laplace transforms are in terms of Tricomi and Kummer confluent hypergeometric functions. We also exhibit the hitting time densities numerically at the end of this paper.     

Ornstein－Uhlenbeck型马氏过程局部时与占位时的存在性

本文考虑Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ型马氏过程的局部时，证明了在一定情形下局部时的存在性，并给出了不存在的反例，同时讨论了这类过程的占位时，指出了在某些限制性条件下，占位时密度的平方可积性．     

On Times to Quasi-stationarity for Birth and Death Processes

The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to the right end of its state space is a sum of independent exponential variables whose parameters are the negatives of the eigenvalues of the underlying generator when the right end is treated as an absorbing state. The exponential variables appear as fastest strong quasi-stationary times for successive dual processes associated to the original absorbed process. As an aftermath, we get an interesting probabilistic representation of the time marginal laws of the process in terms of “local equilibria.”      

On Least Squares Estimation for Stable Nonlinear AR Processes

Following a Markov chain approach, this paper establishes asymptotic properties of the least squares estimator in nonlinear autoregressive (NAR) models. Based on conditions ensuring the stability of the model and allowing the use of a strong law of large number for a wide class of functions, our approach improves some known results on strong consistency and asymptotic normality of the estimator. The exact convergence rate is established by a law of the iterated logarithm. Based on this law and a generalized Akaike's information criterion, we build a strongly consistent procedure for selection of NAR models. Detailed results are given for familiar nonlinear AR models like exponential AR models, threshold models or multilayer feedforward perceptions.