On the Riemann-Hilbert factorization problem for positive definite functions

Dan Kucerovsky; Amir T. P. Najafabadi; Aydin Sarraf

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arXiv · 1506.00977

On the Riemann-Hilbert factorization problem for positive definite functions

Dan Kucerovsky·Amir T. P. Najafabadi·Aydin Sarraf

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Abstract

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 L\'{e}vy processes and we find the distribution of their extrema at a given stopping time.

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Dan Kucerovsky, Amir T. P. Najafabadi, Aydin Sarraf. 2015-06-02. On the Riemann-Hilbert factorization problem for positive definite functions. https://arxiv.org/abs/1506.00977

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