  We study a family of free stochastic processes whose covariance kernels $K$
may be derived as a transform of a tempered measure $\sigma$. These processes
arise, for example, in consideration non-commutative analysis involving free
probability. Hence our use of semi-circle distributions, as opposed to
Gaussians. In this setting we find an orthonormal bases in the corresponding
non-commutative $L^2$ of sample-space. We define a stochastic integral for our
family of free processes.
