Suppose is a mean zero Gaussian process and there exist c and ε such that Prove that there is a version of X that has continuous paths on [0, 1]. Let X be as in. For what values α will X have...

Suppose

is a mean zero Gaussian process and there exist c and ε such that

Prove that there is a version of X that has continuous paths on [0, 1].

Let X be as in. For what values α will X have paths that are Holder continuous of ¨ order α? (α will depend on ε.)