Hitting Probabilities for a Class of Gaussian Processes
Let X={X(t),t∈R}be a Gaussian process with values in Rd defined by X(t)=(X1(t),…,Xd(t))(∀t ∈ R),where X1,…,Xd are independent copies of a real-valued Gaussian process X0={X0(t),t∈R}and E[(X0(t)-X0(s))2]≈ γ2(|t-s|)(f ≈g indicates that there is a constant c,such that c-1g≤f≤cg),γ is a function that satisfies certain conditions and has upper and lower indices.The purpose of this paper is to study the hitting probabilities of the process by using the upper and lower indices of γ.The Haus-dorff measure of the upper bound is determined by the upper indices α*of the function γ,and the capacity of lower bound by the lower indices α*.
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