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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Wiley
2010-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/846320 |
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| author | Marek Slaby |
| author_facet | Marek Slaby |
| author_sort | Marek Slaby |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-388d229205ab4efca1844ddcb70a66a5 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-388d229205ab4efca1844ddcb70a66a52025-02-03T07:23:34ZengWileyJournal of Probability and Statistics1687-952X1687-95382010-01-01201010.1155/2010/846320846320An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent BoundariesMarek Slaby0Department of Mathematics, Computer Science and Physics, Fairleigh Dickinson University, 285 Madison Ave, M-AB2-02, Madison, NJ 07940, USAWe 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.http://dx.doi.org/10.1155/2010/846320 |
| spellingShingle | Marek Slaby An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries Journal of Probability and Statistics |
| title | An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries |
| title_full | An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries |
| title_fullStr | An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries |
| title_full_unstemmed | An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries |
| title_short | An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries |
| title_sort | explicit representation of the extended skorokhod map with two time dependent boundaries |
| url | http://dx.doi.org/10.1155/2010/846320 |
| work_keys_str_mv | AT marekslaby anexplicitrepresentationoftheextendedskorokhodmapwithtwotimedependentboundaries AT marekslaby explicitrepresentationoftheextendedskorokhodmapwithtwotimedependentboundaries |