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Contents of PMS, Vol. 33, Fasc. 1,
pages 121 - 148
 

EXPLICIT SOLUTIONS OF THE EXTENDED SKOROKHOD PROBLEMS IN TIME-DEPENDENT BOUNDED REGIONS WITH ORTHOGONAL REFLECTION FIELDS

Marek Slaby

Abstract: We consider the extended Skorokhod problem for ℝn -valued cądląg functions with the constraining set that changes in time and the reflection field naturally defined by the standard orthonormal basis. We find an explicit formula for the solution of such an extended Skorokhod problem in the case where the evolving constraining set is a region sandwiched between two graphs. We obtain the best Lipschitz constant for the extended Skorokhod map of this type.

2000 AMS Mathematics Subject Classification: Primary 60G17; Secondary 60G07, 60H10, 60J60, 90B05.

Keywords and phrases: Skorokhod problem, extended Skorokhod problem, Skorokhod map, extended Skorokhod map, time-dependent constraining domain.

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