On Free Stochastic Processes and their Derivatives

By Daniel Alpay, Palle E. T. Jorgensen, Guy Salomon. 2013

48 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4b0ef4bc34d5d6bdcbfb0d14350ba623a0b5c98c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Fabrizio Colombo
2. Irene Sabadini
3. Daniel Alpay
4. Daniele C. Struppa
5. Guy Salomon
6. Caterina Stoppato
7. Graziano Gentili
8. Riccardo Ghiloni

In Finance

1. Daniel Alpay

In Statistics and Probability

1. Daniel Alpay
2. Guy Salomon

Citations in the corpus

• The Fock Space in the Slice Hyperholomorphic Setting (2014, background): “The derivative of the function X(t) is studied in [10].”