Switching Identities by Probabilistic Means

J. Backoff; A. M. G. Cox; A. Grass; M. Huesmann

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arXiv · 2002.12840

Switching Identities by Probabilistic Means

J. Backoff·A. M. G. Cox·A. Grass·M. Huesmann

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Abstract

Switching identities have a long history in potential theory and stochastic analysis. In recent work of Cox and Wang, a switching identity was used to connect an optimal stopping problem and the Skorokhod embedding problem (SEP). Typically switching identies of this form are derived using deep analytic connections. In this paper, we prove the switching identities using a simple probabilistic argument, which furthermore highlights a previously unexplored symmetry between the Root and Rost solutions to the SEP.

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J. Backoff, A. M. G. Cox, A. Grass, M. Huesmann. 2020-02-28. Switching Identities by Probabilistic Means. https://arxiv.org/abs/2002.12840

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