Measure-preserving transformations of Volterra Gaussian processes and related bridges

Details Measure-preserving transformations of Volterra Gaussian processes and related bridges Measure-preserving transformations of Volterra Gaussian processes and related bridges

2007-01-30

arxiv.org/abs/math/0701888v2

Mathematics

Probability

21 pages

Scientific paper

We consider Volterra Gaussian processes on [0,T], where T>0 is a fixed time horizon. These are processes of type X_t=\int^t_0 z_X(t,s)dW_s, t\in[0,T], where z_X 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,\infty).

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