Regularity of models associated with Markov jump processes
We consider a jump Markov process , with values in a state space . We suppose that the corresponding infinitesimal generator , hence the law of , depends on a parameter . We prove that several models (filtered or not) associated with are linked, by their regularity according to a certain scheme. In...
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| Published in | Open mathematics (Warsaw, Poland) Vol. 20; no. 1; pp. 911 - 930 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Warsaw
De Gruyter
05.09.2022
De Gruyter Poland |
| Subjects | |
| Online Access | Get full text |
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| Abstract | We consider a jump Markov process
, with values in a state space
. We suppose that the corresponding infinitesimal generator
, hence the law
of
, depends on a parameter
. We prove that several models (filtered or not) associated with
are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model
is equivalent to the local regularity of |
|---|---|
| AbstractList | Abstract
We consider a jump Markov process
X
=
(
X
t
)
t
≥
0
X={\left({X}_{t})}_{t\ge 0}
, with values in a state space
(
E
,
ℰ
)
\left(E,{\mathcal{ {\mathcal E} }})
. We suppose that the corresponding infinitesimal generator
π
θ
(
x
,
d
y
)
,
x
∈
E
{\pi }_{\theta }\left(x,{\rm{d}}y),x\in E
, hence the law
P
x
,
θ
{{\mathbb{P}}}_{x,\theta }
of
X
X
, depends on a parameter
θ
∈
Θ
\theta \in \Theta
. We prove that several models (filtered or not) associated with
X
X
are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model
(
π
θ
(
x
,
d
y
)
)
θ
∈
Θ
{\left({\pi }_{\theta }\left(x,{\rm{d}}y))}_{\theta \in \Theta }
is equivalent to the local regularity of
(
P
x
,
θ
)
θ
∈
Θ
{\left({{\mathbb{P}}}_{x,\theta })}_{\theta \in \Theta }
. We consider a jump Markov process , with values in a state space . We suppose that the corresponding infinitesimal generator , hence the law of , depends on a parameter . We prove that several models (filtered or not) associated with are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model is equivalent to the local regularity of We consider a jump Markov process X=(Xt)t≥0X={\left({X}_{t})}_{t\ge 0}, with values in a state space (E,ℰ)\left(E,{\mathcal{ {\mathcal E} }}). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E{\pi }_{\theta }\left(x,{\rm{d}}y),x\in E, hence the law Px,θ{{\mathbb{P}}}_{x,\theta } of XX, depends on a parameter θ∈Θ\theta \in \Theta . We prove that several models (filtered or not) associated with XX are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model (πθ(x,dy))θ∈Θ{\left({\pi }_{\theta }\left(x,{\rm{d}}y))}_{\theta \in \Theta } is equivalent to the local regularity of (Px,θ)θ∈Θ{\left({{\mathbb{P}}}_{x,\theta })}_{\theta \in \Theta }. We consider a jump Markov process X=(Xt)t≥0, with values in a state space (E,ℰ). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E, hence the law Px,θ of X, depends on a parameter θ∈Θ. We prove that several models (filtered or not) associated with X are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model (πθ(x,dy))θ∈Θ is equivalent to the local regularity of (Px,θ)θ∈Θ. |
| Author | Jedidi, Wissem |
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| Snippet | We consider a jump Markov process
, with values in a state space
. We suppose that the corresponding infinitesimal generator
, hence the law
of
, depends on a... Abstract We consider a jump Markov process X = ( X t ) t ≥ 0 X={\left({X}_{t})}_{t\ge 0} , with values in a state space ( E , ℰ ) \left(E,{\mathcal{ {\mathcal... We consider a jump Markov process X=(Xt)t≥0, with values in a state space (E,ℰ). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E, hence... We consider a jump Markov process X=(Xt)t≥0X={\left({X}_{t})}_{t\ge 0}, with values in a state space (E,ℰ)\left(E,{\mathcal{ {\mathcal E} }}). We suppose that... |
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| StartPage | 911 |
| SubjectTerms | 62M20 65C20 Fisher information matrix Hellinger integrals infinitesimal generator isomorphism jump Markov process likelihood processes local regularity Markov processes randomization Regularity regularity of models |
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| Title | Regularity of models associated with Markov jump processes |
| URI | http://www.degruyter.com/doi/10.1515/math-2022-0482 https://www.proquest.com/docview/2709780434 https://doaj.org/article/2ec22ca7bb3c42b3aa2a5ef860ac75a9 |
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