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 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.Small ball probabilities Gaussian Markov processes Brownian motion