摘要
Let X(t) be an N parameter generalized Lévy sheet taking values in Rd with a lower index α,sR = {(s,t] = ∏iN=1(si,ti],si ＜ ti},E(x,Q) = {t ∈ Q: X(t) = x},Q ∈ sR be the level set of X at x and X(Q) = {x: (E)t ∈ Q such that X(t) = x} be the image of X on Q.In this paper,the problems of the existence and increment size of the local times for X(t) are studied.In addition,the Hausdorff dimension of E(x,Q) and the upper bound of a uniform dimension for X(Q) are also established.
Let X(t) be an N parameter generalized Levy sheet taking values in Rd with a lower index a, R={(s,t] =∏i=1N(si,ti)],si<ti}. E(x,Q) = {t∈Q : X(t) = x},Q∈R be the level set of X at x and X(Q) = {x : (?)t∈Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x,Q) and the upper bound of a uniform dimension for X(Q) are also established.
基金
This work was partially supported by the National Natural Science Foundation of China(Grant No.10571159)
China Postdoctoral Science Foundation.
