Moments of random variables: a systems-theoretic interpretation
File(s)
Accepted version
Author(s)
Padoan, Alberto
Astolfi, Alessandro
Type
Journal Article
Abstract
Moments of continuous random variables admitting a probability density function are studied. We show that, under certain assumptions, the moments of a random variable can be characterised in terms of a Sylvester equation and of the steady-state output response of a specific interconnected system. This allows to interpret well-known notions and results of probability theory and statistics in the language of systems theory, including the sum of independent random variables, the notion of mixture distribution and results from renewal theory. The theory developed is based on tools from the center manifold theory, the theory of the steady-state response of nonlinear systems, and the theory of output regulation. Our formalism is illustrated by means of several examples and can be easily adapted to the case of discrete and of multivariate random variables.
Date Issued
2019-11-01
Date Acceptance
2018-12-30
Citation
IEEE Transactions on Automatic Control, 2019, 64 (11), pp.4407-4422
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
4407
End Page
4422
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
64
Issue
11
Copyright Statement
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
Commission of the European Communities
Identifier
https://ieeexplore.ieee.org/document/8637762
Grant Number
664639
Subjects
Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Random variables
Probability density function
Linear systems
Steady-state
Tools
Probability distribution
Differential equations
interpolation
nonlinear systems
probability
random variables
statistics
transfer functions
STEADY-STATE RESPONSE
MODEL-REDUCTION
DISCRETE
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status
Published
Date Publish Online
2019-02-08