SELF-INTERSECTION LOCAL TIME OF ADDITIVE LEVY PROCESS

This article discusses the problem of existence of jointly continuous self-intersection local time for an additive levy process. Here, 'local time' is understood in the sense of occupation density, and by an additive Levy process the authors mean a process X = {X(t),t∈ R+N} which has the decomposition X = Xi X2 … XN, each Xl has the lower index αl, α= min{α1,…, αN}. Let Z = (Xt2 - Xt1, …, Xtr - Xtr-1). They prove that if Nrα > d(r-1), then a jointly continuous local time of Z, i.e. the self-intersection local time of X, can be obtained.

Shift control method for the local time at descendi ngnode based on sun-synchronous orbit satellite

This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.

ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES

In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion

LOCAL TIME ANALYSIS OF ADDITIVE LVY PROCESSES WITH DIFFERENT LVY EXPONENTS

Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1） ＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.

REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

Local Time of Additive Levy Process

We studied the problem of existence of jointly continuous local time for an additive process. Here, 'local time' is understood in the sence of occupation density, and by an additive Levy process we mean a process X = {X(t), t ∈ R^d_+ ) } which has the decomposition X= X_1, X_2 ... X_N. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can he obtained via Berman's method.

SOME LIMIT PROPERTIES OF LOCAL TIME FOR RANDOM WALK

Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.

SOME RESULTSON LAG INCREMENTSOF PRINCIPAL VALUE OF BROWNIAN LOCAL TIME

Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1 983

Local times of linear multifractional stable sheets

Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.

Local time and Tanaka formula of G-martingales

The objective of this paper is to study the local time and Tanaka formula of symmetric G-martingales.We introduce the local time of G-martingales and show that it belongs to the G-expectation space LG^2(ΩT).By a localization argument,we obtain the bicontinuous modification of local time.Furthermore,we give the Tanaka formula for convex functions of G-martingales.

Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions

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.

Derivatives of Intersection Local Time for Two Independent Symmetricα-stable Processes

In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient condition for the existence of the derivatives,which makes us obtain the exponential integrability and H?lder continuity.Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin.Moreover,we also study the power variation of the derivatives.

Study on the local time asymmetry of the Earth's ring currents based on multiple low-Earth-orbit satellite magnetic observations

The azimuthal morphology of Earth's ring currents has consistently shown asymmetry during extreme space weather events at low latitudes,particularly during geomagnetic storms.A dawn-dusk pattern has been detected during the storm main phase through near-Earth and in-situ magnetic measurements.This asymmetry is believed to arise from asymmetric solar windmagnetosphere coupling and is linked to the closure of the ring current.Recent evidence has confirmed the existence of asymmetric ring currents during quiet times and the storm recovery phase.This phenomenon may be closely related to the evolution of ring currents,including plasma injection and decay processes.In this study,the local time asymmetry of the ring current is estimated using data from low-Earth-orbit Swarm and Macao Science Satellite-1(MSS-1)missions.Spherical harmonics models are developed to quantify the magnetic field of ring currents through external Gauss coefficients during both quiet periods and the storm recovery phase.Several features of dawn-dusk asymmetry are observed in various cases in different months.(1)The maximum difference in magnetic value across local time ranges from 3 to 10 nT,showing relative invariance compared with various Sym-H levels.(2)Stronger magnetic signals are detected at the premidnight sector during quiet times and at the afternoon sector during the storm recovery phase.(3)Magnetic perturbations remain at a lower level during the postmidnight and morning sectors.Although the pattern of local time asymmetry differs between quiet times and the recovery phase,dawn-dusk asymmetry remains the most pronounced feature,affecting the trapping and loss of charged particles in the inner magnetosphere.Combining Swarm and MSS-1 magnetic observations can enable convenient monitoring of the detailed azimuthal local time effects of the ring current at various disturbance levels in the future.

Smoothness of local times and self-intersection local times of Gaussian random fields

This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.

Self-intersection local times and collision local times of bifractional Brownian motions

In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.

Smoothness for the collision local times of bifractional Brownian motions

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

基于TimeSVD++与DPC的推荐算法研究

针对使用奇异值分解(SVD)方法时需要填充矩阵的内容较多以及K-means算法受到K值的影响且数据集形状限制等问题,提出一种将TimeSVD++与改进的密度峰值聚类结合的方法。首先在SVD++的基础上引入参数时间因子,构建TimeSVD++模型;其次,采用将相似系数引入高斯核函数的方法,对密度峰聚类算法中的局部密度公式进行修正;引入信息熵确定最优截断距离,最后在数据集MovieLens-1M和MovieLens-100k上验证,并将实验结果与其它算法进行对比。结果表明:所提出的方法在MAE,RMSE,Recall和F1值指标上均优于其它的算法。

On the Collision Local Time of Fractional Brownian Motions

In this paper, the existence and smoothness of the collision local time are proved for two independent fractional Brownian motions, through L^2 convergence and Chaos expansion. Furthermore, the regularity of the collision local time process is studied.

Theoretical development for DSMC local time stepping technique

The direct simulation Monte Carlo(DSMC) method is the most mature and wildly used approach for nonequilibrium gas flow simulation.The phenomenological nature of this method brings flexibility to the computation algorithms.In this study,the theoretical foundations to decouple the molecular motion and collision within a time step are discussed in detail,which can be treated as criterions for the DSMC algorithms.Based on the theoretical developments,an improved local time stepping scheme is proposed,which specifies the movement time attribute and the collision time attribute for each representative particle.A free flow about a sphere body is considered as an example,which is compared with the calculations using the published local time stepping technique.The results show that the improved local time scheme is valid and is promising in realizing flow structures with strong variations.