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The structure of entrance laws for time-inhomogeneous Ornstein–Uhlenbeck processes with Lévy noise in Hilbert spaces
- Source :
- Infinite Dimensional Analysis, Quantum Probability and Related Topics. 24:2150011
- Publication Year :
- 2021
- Publisher :
- World Scientific Pub Co Pte Lt, 2021.
-
Abstract
- This paper is about the structure of all entrance laws (in the sense of Dynkin) for time-inhomogeneous Ornstein–Uhlenbeck processes with Lévy noise in Hilbert state spaces. We identify the extremal entrance laws with finite weak first moments through an explicit formula for their Fourier transforms, generalizing corresponding results by Dynkin for Wiener noise and nuclear state spaces. We then prove that an arbitrary entrance law with finite weak first moments can be uniquely represented as an integral over extremals. It is proved that this can be derived from Dynkin’s seminal work “Sufficient statistics and extreme points” in Ann. Probab. 1978, which contains a purely measure theoretic generalization of the classical analytic Krein–Milman and Choquet Theorems. As an application, we obtain an easy uniqueness proof for [Formula: see text]-periodic entrance laws in the general periodic case. A number of further applications to concrete cases are presented.
- Subjects :
- Statistics and Probability
Levy processes
Applied Mathematics
processes
010102 general mathematics
integral representations
Hilbert space
Structure (category theory)
Statistical and Nonlinear Physics
Ornstein–Uhlenbeck process
State (functional analysis)
evolution system of measures
01 natural sciences
Lévy process
010104 statistics & probability
Levy noise
symbols.namesake
Entrance laws
Law
symbols
Ornstein Uhlenbeck
0101 mathematics
Mathematical Physics
Mathematics
Subjects
Details
- ISSN :
- 17936306 and 02190257
- Volume :
- 24
- Database :
- OpenAIRE
- Journal :
- Infinite Dimensional Analysis, Quantum Probability and Related Topics
- Accession number :
- edsair.doi.dedup.....7d1bad1e50e05fd1ba1bde2358d86127