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Graphical modeling of stochastic processes driven by correlated noise

Mogensen, Søren Wengel LU and Hansen, Niels Richard (2022) In Bernoulli 28(4). p.3028-3050
Abstract

We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated noise processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolyno-mially as a function of the size of the node set in the graph. We show that deciding Markov equivalence of graphs from this class is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Graphical models, local independence, Markov equivalence, Ornstein–Uhlenbeck processes, stochastic processes
in
Bernoulli
volume
28
issue
4
pages
23 pages
publisher
Chapman and Hall
external identifiers
  • scopus:85136269564
ISSN
1350-7265
DOI
10.3150/21-BEJ1446
language
English
LU publication?
yes
id
70999c21-f255-4766-814d-b657eb347291
date added to LUP
2022-09-05 15:06:45
date last changed
2022-09-05 15:06:45
@article{70999c21-f255-4766-814d-b657eb347291,
  abstract     = {{<p>We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated noise processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolyno-mially as a function of the size of the node set in the graph. We show that deciding Markov equivalence of graphs from this class is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.</p>}},
  author       = {{Mogensen, Søren Wengel and Hansen, Niels Richard}},
  issn         = {{1350-7265}},
  keywords     = {{Graphical models; local independence; Markov equivalence; Ornstein–Uhlenbeck processes; stochastic processes}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{3028--3050}},
  publisher    = {{Chapman and Hall}},
  series       = {{Bernoulli}},
  title        = {{Graphical modeling of stochastic processes driven by correlated noise}},
  url          = {{http://dx.doi.org/10.3150/21-BEJ1446}},
  doi          = {{10.3150/21-BEJ1446}},
  volume       = {{28}},
  year         = {{2022}},
}