Extensions of the fractional Brownian fields are constructed over
a complete Riemannian manifold. This construction is carried out for the full
range of the Hurst parameter α ∈ (0, 1). In particular, we establish existence,
distributional scaling (self-similiarity), stationarity of the increments, and almost
sure H¨older continuity of sample paths....
This dissertation presents some results from various areas of probability theory, the unifying theme being the use of functional analytic intuition and techniques. We first give a result regarding the existence of certain stochastic integral representations for Banach space valued Gaussian random variables. Next we give a spectral geometric construction...