Measure-preserving transformations of Volterra Gaussian processes and related bridges

We consider Volterra Gaussian processes on [0, T ], where T > 0 is a fixed time horizon. These are processes of type Xt = R t 0 zX(t, s)dWs, t ∈ [0, T ], where zX is a square-integrable kernel, and W is a standard Brownian motion. An example is fractional Brownian motion. By using classical techniques from operator theory, we derive measure-preserving transformations of X, and their inherently related bridges of X. As a closely connected result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale over [0,∞). MSC: 60G15; 37A05; 42C10; 60G44