### The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces

Majid NR, Röckner M (2021)
Infinite Dimensional Analysis, Quantum Probability and Related Topics 24(02): 2150011.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Majid, Narges Rezvani; Röckner, MichaelUniBi
Einrichtung
Abstract / Bemerkung
This paper is about the structure of all entrance laws (in the sense of Dynkin) for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy 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 T-periodic entrance laws in the general periodic case. A number of further applications to concrete cases are presented.
Stichworte
Entrance laws; evolution system of measures; Ornstein Uhlenbeck; processes; Levy processes; integral representations
Erscheinungsjahr
2021
Zeitschriftentitel
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Band
24
Ausgabe
02
Art.-Nr.
2150011
ISSN
0219-0257
eISSN
1793-6306
Page URI
https://pub.uni-bielefeld.de/record/2956999

### Zitieren

Majid NR, Röckner M. The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2021;24(02): 2150011.
Majid, N. R., & Röckner, M. (2021). The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 24(02), 2150011. https://doi.org/10.1142/S0219025721500119
Majid, N. R., and Röckner, M. (2021). The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics 24:2150011.
Majid, N.R., & Röckner, M., 2021. The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 24(02): 2150011.
N.R. Majid and M. Röckner, “The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 24, 2021, : 2150011.
Majid, N.R., Röckner, M.: The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 24, : 2150011 (2021).
Majid, Narges Rezvani, and Röckner, Michael. “The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces”. Infinite Dimensional Analysis, Quantum Probability and Related Topics 24.02 (2021): 2150011.

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