English

On free stochastic processes and their derivatives

Operator Algebras 2013-11-14 v1 Functional Analysis Probability

Abstract

We study a family of free stochastic processes whose covariance kernels KK may be derived as a transform of a tempered measure σ\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 L2L^2 of sample-space. We define a stochastic integral for our family of free processes.

Keywords

Cite

@article{arxiv.1311.3239,
  title  = {On free stochastic processes and their derivatives},
  author = {Daniel Alpay and Palle Jorgensen and Guy Salomon},
  journal= {arXiv preprint arXiv:1311.3239},
  year   = {2013}
}
R2 v1 2026-06-22T02:06:55.105Z