Small ball probabilities for Gaussian Markov processes under the Lp-norm

Let {X(t); 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} be a real-valued continuous Gaussian Markov process with mean zero and covariance [sigma](s,t)=EX(s)X(t)[not equal to]0 for 0<s, t<1. It is known that we can write [sigma](s,t)=G(min(s,t))H(max(s,t)) with G>0, H>0 and G/H nondecreasing on the interval (0,1). We show that for the Lp-norm on C[0,1], 1[less-than-or-equals, slant]p[less-than-or-equals, slant][infinity]and its various extensions.