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 a...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.展开更多
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) △=...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}.展开更多
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 a...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.展开更多
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 proc...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.展开更多
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...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.展开更多
基金Supported by the National Natural Science Foundation and the Doctoral Programme Foundation of China.
文摘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.
文摘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}.
基金Supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(71221061)National Natural Science Foundation of China(11171101)+3 种基金National Social Science Fund of China(11BTJ01115BJY122)Social Sciences Foundation of Ministry of Education of China(12YJAZH173)Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘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.
基金the National Natural Science Foundation of China
文摘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.
文摘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.