Graphical modeling of stochastic processes driven by correlated noise
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Graphical modeling of stochastic processes driven by correlated noise. / Mogensen, Søren Wengel; Hansen, Niels Richard.
I: Bernoulli, Bind 28, Nr. 4, 2022, s. 3028-3050.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Graphical modeling of stochastic processes driven by correlated noise
AU - Mogensen, Søren Wengel
AU - Hansen, Niels Richard
N1 - Publisher Copyright: © 2022 ISI/BS.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Graphical models
KW - local independence
KW - Markov equivalence
KW - Ornstein–Uhlenbeck processes
KW - stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=85136269564&partnerID=8YFLogxK
U2 - 10.3150/21-BEJ1446
DO - 10.3150/21-BEJ1446
M3 - Journal article
AN - SCOPUS:85136269564
VL - 28
SP - 3028
EP - 3050
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 4
ER -
ID: 318815736