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.

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}.

The mean correcting martingale measures for exponential additive processes

The mean correcting martingale measure for the stochastic process defined as the exponential of an additive process is constructed. Necessary and sufficient conditions for the existence of mean correcting martingale are also obtained. The investigation of this paper will establish a unified way that is applicable both to the case of Ldvy processes and that of the sums of independent random variables. As an application, we present the necessary and sufficient conditions that the discounted stock price process is a martingale.

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.

Ligand Size Effect on PdLn Oxidative Addition with Aryl Bromide： A DFT Study

The process and mechanism of the ligand volume controlled Pd（PR3）2 （PR3=PH3, PMe3, and PtBu3） oxidative addition with aryl bromide were investigated, using density functional theory method with the conductor-like screening model. Association pathway and dissocia-tion pathway were investigated by the comparison of several energies. The cleavage energy of Pd（PR3）2 complex was calculated, as well as the oxidative addition reaction barrier energy of Pd（PR3）n （n=1,2） with aryl bromide in N,N-dimethylformamide solvent. This study proved that the ligands volume possessed a great impact on the mechanism of oxidative addition： less bulky ligand palladium associated with aryl bromide via two donor ligands,but larger bulky ligand palladium coordinated via monoligand.

Influence of Process Parameters and Sr Addition on the Microstructure and Casting Defects of LPDC A356 Alloy for Engine Blocks

The effects of Sr addition and pressure increase on the microstructure and casting defects of a low-pressure die cast （LPDC） AISi7Mg0.3 alloy have been studied. Metallographic and image analysis techniques have been used to quantitatively examine the microstructural changes and the amount of porosity occurring at different Sr levels and pressure parameters. The results indicate that an increase in the filling pressure induces lower heat dissipation of the liquid close to the die/core surfaces, with the formation of slightly greater dendrite arms and coarser eutectic Si particles. On the other hand, the increase in the Sr level leads to finer microstructural scale and eutectic Si. The analysed variables, within the experimental conditions, do not affect the morphology of eutectic Si particles. Higher applied pressure and Sr content generate castings with lower amount of porosiW. However, as the filling pressure increases the flow of metal inside the die cavity is more turbulent, leading to the formation of oxide films and cold shots. In the analysed range of experimental conditions, the design of experiment methodology and the analysis of variance have been used to develop statistical models that accurately predict the average size of secondary dendrite arm spacing and the amount of porosity in the low-pressure die cast AISiTMg0.3 alloy.