publication . Preprint . 2015

Poisson Processes in Free Probability

An, Guimei; Gao, Mingchu;
Open Access English
  • Published: 09 Jun 2015
We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisson process. A Karhunen-Loeve expansion theorem for centered free Poisson processes is proved. We generalize free Poisson processes to a notion of free Poisson random measures...
free text keywords: Mathematics - Operator Algebras, 46L54
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