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arXiv · 1311.3239

On free stochastic processes and their derivatives

Daniel Alpay·Palle Jorgensen·Guy Salomon
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Abstract

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 non-commutative $L^2$ of sample-space. We define a stochastic integral for our family of free processes.

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Daniel Alpay, Palle Jorgensen, Guy Salomon. 2013-11-13. On free stochastic processes and their derivatives. https://arxiv.org/abs/1311.3239

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