On the Riemann-Hilbert factorization problem for positive definite functions

We give several general theorems concerning positive definite solutions of Riemann-Hilbert problems on the real line. Furthermore, as an example, we apply our theory to the characteristic function of a class of Lévy processes and we find the distribution of their extrema at a given stopping time.

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2016-09, Vol.20 (3), p.743-754
Main Authors: Kučerovský, Dan, Najafabadi, Amir T. P., Sarraf, Aydin
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Fourier transforms
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Random variables
Studies
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Summary:We give several general theorems concerning positive definite solutions of Riemann-Hilbert problems on the real line. Furthermore, as an example, we apply our theory to the characteristic function of a class of Lévy processes and we find the distribution of their extrema at a given stopping time.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-015-0384-y