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.

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.

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.

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.

Some Results on Fractional Brownian Sheets and Their Local Times

Let B0^H = {B0^H（t）,t ∈ R＋^N） be a real-valued fractional Brownian sheet. Define the （N,d）- Gaussian random field B^H by B^H（t） = （B1^H（t）,...,Bd^H（t）） t ∈ R＋^N, where B1^H, ..., Bd^H are independent copies of B0^H. The existence and joint continuity of local times of B^H is proven in some given conditions in [22]. We then study further properties of the local times of B^H, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].

Results on Local Times of a Class of Multiparameter Gaussian Processes

In this paper, we introduce a class of Gaussian processes Y={Y（t）：t∈R^N},the so called hifractional Brownian motion with the indcxes H=（H1,…,HN）and α. We consider the （N, d, H, α） Gaussian random field x（t） = （x1 （t）,..., xd（t））,where X1 （t）,…, Xd（t） are independent copies of Y（t）, At first we show the existence and join continuity of the local times of X = {X（t）, t ∈ R＋^N}, then we consider the HSlder conditions for the local times.

Thermosphere joint observations by TM-1 constellations and Swarm-B during the April 2023 geomagnetic storm

The response of thermosphere density to geomagnetic storms is a complicated physical process.Multi-satellite joint observations at the same altitude but different local times(LTs)are important for understanding this process;however,until now such studies have hardly been done.In this report,we analyze in detail the thermosphere mass density response at 510 km during the April 23−24,2023 geomagnetic storm using data derived from the TM-1(TianMu-1)satellite constellation and Swarm-B satellites.The observations show that there were significant LT differences in the hemispheric asymmetry of the thermosphere mass density during the geomagnetic storm.Densities observed by satellite TM02 at nearly 11.3 and 23.3 LTs were larger in the northern hemisphere than in the southern.The TM04 dayside density observations appear to be almost symmetrical with respect to the equator,though southern hemisphere densities on the nightside were higher.Swarm-B data exhibit near-symmetry between the hemispheres.In addition,the mass density ratio results show that TM04 nightside observations,TM02 data,and Swarm-B data all clearly show stronger effects in the southern hemisphere,except for TM04 on the dayside,which suggest hemispheric near-symmetry.The South-North density enhancement differences in TM02 and TM04 on dayside can reach 130%,and Swarm-B data even achieve 180%difference.From the observations of all three satellites,large-scale traveling atmospheric disturbances(TADs)first appear at high latitudes and propagate to low latitudes,thereby disturbing the atmosphere above the equator and even into the opposite hemisphere.NRLMSISE00 model simulations were also performed on this geomagnetic storm.TADs are absent in the NRLMSISE00 simulations.The satellite data suggest that NRLMSISE00 significantly underestimates the magnitude of the density response of the thermosphere during geomagnetic storms,especially at high latitudes in both hemispheres.Therefore,use of the density simulation of NRLMSISE00 may lead to large errors in satellite drag calculations and orbit predictions.We suggest that the high temporal and spatial resolution of direct density observations by the TM-1 constellation satellites can provide an autonomous and reliable basis for correction and improvement of atmospheric models.

Effect of interplanetary magnetic field B_(x)on the polar electrojets as observed by CHAMP and Swarm satellites

Based on 16 years of magnetic field observations from CHAMP and Swarm satellites,this study investigates the influence of the Interplanetary Magnetic Field(IMF)Bx component on the location and peak current density of the polar electrojets(PEJs).We find that the IMF Bx displays obvious local time,seasonal,and hemispherical effects on the PEJs,as follows:(1)Compared to other local times,its influence is weakest at dawn and dusk.(2)In the midnight sectors of both hemispheres,the IMF Bx tends to amplify the westward PEJ when it is<0 in the Northern Hemisphere and when it is>0 in the Southern Hemisphere;this effect is relatively stronger in the local winter hemisphere.(3)At noontime,the IMF Bx intensifies the eastward current when it is<0 in the Northern Hemisphere;in the Southern Hemisphere when it is>0,it reduces the westward current;this effect is notably more prominent in the local summer hemisphere.(4)Moreover,the noontime eastward current shifts towards higher latitudes,while the midnight westward current migrates towards lower latitudes when IMF Bx is<0 in the Northern Hemisphere and when it is>0 in the Southern Hemisphere.

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.

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.

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}.

Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes

Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in- cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal component analysis. In this approach, mutual information estimation and Bayesian information criterion （BIC） are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation （BP） network is applied whose input is multivar- iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis （LKPCA） model for incipient fault prognosis. The new method has been exemplified in a sim- ple nonlinear process and the complicated Tennessee Eastman （TE） benchmark process. The results indicate that the new method has suoerioritv in the fault prognosis sensitivity over other traditional fault prognosis methods.

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

Improving entanglement of assistance by local parity–time symmetric operation

We investigate entanglement of assistance without and with decoherence using a local non-Hermitian operation, i.e.,parity–time(PT) symmetric operation. First we give the explicit expressions of entanglement of assistance for a general W-like state of a three-qubit system under a local parity–time symmetric operation. Then for a famous W state without decoherence, we find that entanglement of assistance shared by two parties can be obviously enhanced with the assistance of the third party by a local parity–time symmetric operation. For the decoherence case, we provide two schemes to show the effects of local parity–time symmetric operation on improvement of entanglement of assistance against amplitude damping noise. We find that for the larger amplitude damping case the scheme of PT symmetric operation performed on one of two parties with the influence of noise is superior to that of PT symmetric operation performed on the third party without the influence of noise in suppressing amplitude damping noise. However, for the smaller amplitude damping case the opposite result is given. The obtained results imply that the local PT symmetric operation method may have potential applications in quantum decoherence control.

On Local Integrated Cosine Functions

Suppose X is a Banach space, and A is a closed operator. We give some equivalent conditions between A generating a local integrated cosine functions and the existence of solutions of abstract Cauchy problems.