It was shown in Mishura etal. (Stochastic Process. AppL 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to cover a wide class of Gaussian processes. In particular, we consider a wide class of processes that are Holder continuous of order alpha > 1/2 and show that only local properties of the covariance function play role for such results.
- Follmer integral
- Gaussian processes
- generalised Lebesgue Stieltjes integral
- integral representation
- SMALL BALL PROBABILITIES