On free stochastic processes and their derivatives

Daniel Alpay, Palle Jorgensen, Guy Salomon

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

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 of non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal basis in the corresponding non-commutative L2 of sample-space. We define a stochastic integral for our family of free processes.

Original languageEnglish
Pages (from-to)3392-3411
Number of pages20
JournalStochastic Processes and their Applications
Volume124
Issue number10
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Convolution algebra
  • Non-commutative stochastic distributions
  • Non-commutative white noise space

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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