Non-commutative stochastic distributions and applications to linear systems theory

Daniel Alpay; Guy Salomon

doi:10.1016/j.spa.2013.02.005

Non-commutative stochastic distributions and applications to linear systems theory

Daniel Alpay, Guy Salomon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.

Original language	English
Pages (from-to)	2303-2322
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	123
Issue number	6
DOIs	https://doi.org/10.1016/j.spa.2013.02.005
State	Published - 25 Mar 2013

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/j.spa.2013.02.005

Cite this

@article{e4279f8ff9bc4f23b28028080caf1546,

title = "Non-commutative stochastic distributions and applications to linear systems theory",

abstract = "In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.",

keywords = "Convolution algebra, Non-commutative stochastic distributions, Non-commutative white noise space",

author = "Daniel Alpay and Guy Salomon",

note = "Funding Information: D. Alpay thanks the Earl Katz family for endowing the chair which supported his research, and the Binational Science Foundation Grant number 2010117 .",

year = "2013",

month = mar,

day = "25",

doi = "10.1016/j.spa.2013.02.005",

language = "English",

volume = "123",

pages = "2303--2322",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "6",

}

TY - JOUR

T1 - Non-commutative stochastic distributions and applications to linear systems theory

AU - Alpay, Daniel

AU - Salomon, Guy

N1 - Funding Information: D. Alpay thanks the Earl Katz family for endowing the chair which supported his research, and the Binational Science Foundation Grant number 2010117 .

PY - 2013/3/25

Y1 - 2013/3/25

N2 - In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.

AB - In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.

KW - Convolution algebra

KW - Non-commutative stochastic distributions

KW - Non-commutative white noise space

UR - http://www.scopus.com/inward/record.url?scp=84875160916&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2013.02.005

DO - 10.1016/j.spa.2013.02.005

M3 - Article

AN - SCOPUS:84875160916

SN - 0304-4149

VL - 123

SP - 2303

EP - 2322

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 6

ER -

Non-commutative stochastic distributions and applications to linear systems theory

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this