An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries
We consider the extended Skorokhod problem for real-valued càdlàg functions with the constraining interval [𝛼,𝛽], where 𝛼 and 𝛽 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, 𝐽1 and 𝑀1, met...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2010-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/846320 |
| Summary: | We consider the extended Skorokhod problem for real-valued càdlàg functions with the constraining interval [𝛼,𝛽], where 𝛼 and 𝛽 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, 𝐽1 and 𝑀1, 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. |
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| ISSN: | 1687-952X 1687-9538 |