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 language | English |
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Pages (from-to) | 3392-3411 |
Number of pages | 20 |
Journal | Stochastic Processes and their Applications |
Volume | 124 |
Issue number | 10 |
DOIs | |
State | Published - 1 Jan 2014 |
Externally published | Yes |
Keywords
- Convolution algebra
- Non-commutative stochastic distributions
- Non-commutative white noise space
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics