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Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence
- Source :
- Stochastic Processes and their Applications., Stochastic Processes and their Applications, Stochastic Processes and their Applications, Elsevier, In press, 144, pp.173-201, Stochastic Processes and their Applications, 2022, 144, pp.173-201. ⟨10.1016/j.spa.2021.11.005⟩
- Publication Year :
- 2022
-
Abstract
- Consider the Langevin process, described by a vector (position,momentum) in $\mathbb{R}^{d}\times\mathbb{R}^d$. Let $\mathcal O$ be a $\mathcal{C}^2$ open bounded and connected set of $\mathbb{R}^d$. We prove the compactness of the semigroup of the Langevin process absorbed at the boundary of the domain $D:=\mathcal{O}\times\mathbb{R}^d$. We then obtain the existence of a unique quasi-stationary distribution (QSD) for the Langevin process on $D$. We also provide a spectral interpretation of this QSD and obtain an exponential convergence of the Langevin process conditioned on non-absorption towards the QSD.
- Subjects :
- Statistics and Probability
Stationary distribution
Semigroup
Applied Mathematics
010102 general mathematics
Mathematical analysis
Probability (math.PR)
Boundary (topology)
01 natural sciences
Domain (mathematical analysis)
Mathematics - Spectral Theory
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
010104 statistics & probability
Compact space
Position (vector)
Modeling and Simulation
Bounded function
FOS: Mathematics
Uniqueness
0101 mathematics
Spectral Theory (math.SP)
Mathematics - Probability
Mathematics
[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
Subjects
Details
- ISSN :
- 03044149 and 1879209X
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications.
- Accession number :
- edsair.doi.dedup.....4188d776d535e400a2f03c05e9a3967f
- Full Text :
- https://doi.org/10.1016/j.spa.2021.11.005