The Fractal Dimensions For Image Sets And Graph Sets Of A Class Of Stochastic Process With Several Indexes

In this paper,we Let {X(t,w) : t ∈ R~N) be a stochastic process taking values in R~d and with its paths continuous and with the condition: Let 0 < a < 1, M > 0,β≥ d be constants such thatWe obtain the best upper bounds of Hausdorff dimension of the image sets , the graph sets and the level sets about X :moreover, with the condition: Let a,a,d' > 0 be constants such that P(|X(t) - X(s)| <|t- s|~ax) ≤ ax~d' t,s ∈R~N,x≥0We obtain the best under bounds of Hausdorff dimension of the image sets , the graph sets about X :These results extend the results of Zhao Xingqiu.