The Local Times Of Multi-parameter Processes With Stable Components And Additive Stable Components

In 1981,Ehm sloved the existence and the smoothness properties and the asymptotic behavior of the local time. In 2003,Xiao etc. discussed the correspend problems of the local time . Jain, Pruitt and Taylor discussed the one-parameter processes with stable components, but it doesn't exist local times. However, few papers discuss about the properties of the local time on multi- parameter processes with stable or additive stable components.In this paper the local times on multi-parameter processes with stable or additive stable components are discussed. The main results are as follows:I) The existence and the continuousness properties of the local time for multi-parameter processes with stable components.(N,dh,ah) stable processes Respectively; d = We obtain the result as follows:If then almost surely X has jointly continuous local times II) Holder laws for local times increments on multi-parameter processes with stable components.the local times of We obtain the results as follows :1) Let , then there is a finite constant c1 > 0, such that for every s > s02) Let N > B , then there is a finite constant c2 > 0 , such that for anyIII) The existence and the continuousness properties of the local time for multi- parameter processes with additive stable components.Let X = (X1,X2, ..., Xh), where X1, X2, ..., Xh are independent; Xi be an additive stable processes in Rdi, that is Xi(t) = Xi1(t1) +i2(t2) +... + XiN(tN), t = (t1,...,tN) RN+, where Xij be stable- (1,di,aij) (1 < i < h, 1 < j < N);d = We obtain the result as follows:If almost surely X has jointly continuous local times...