An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries

Marek Slaby

Journal of Probability and Statistics, 2010, vol. 2010, 1-18

Abstract:

We consider the extended Skorokhod problem for real-valued càdlàg functions with the constraining interval [ ð ›¼ , ð ›½ ] , where ð ›¼ and ð ›½ change in time as values of two càdlàg functions. We find an explicit form of the solution and discuss its continuity properties with respect to the uniform, ð ½ 1 and ð ‘€ 1 , metrics on the space of càdlàg functions. We develop a useful technique of extending known results for the Skorokhod maps onto the larger class of extended Skorokhod maps.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:846320

DOI: 10.1155/2010/846320

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