We study a family of free stochastic processes whose covariance kernels K may be derived as a transform of a tempered measure σ. 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 noncommutative L2 of sample-space. We define a stochastic integral for our family of free processes.
D. Alpay, P. Jorgensen and G. Salomon. On free stochastic processes and their derivatives. Stochastic Processes and their Applications, vo. 214 (2014), 3392-3411
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