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Contents of PMS, Vol. 30, Fasc. 1,
pages 29 - 60
 

EXPLICIT REPRESENTATION OF THE SKOROKHOD MAP WITH TIME DEPENDENT BOUNDARIES

Marek Slaby

Abstract: An explicit formula for the Skorokhod type reflection map for real-valued cądląg functions is developed in the general case of constraining set [a,b], where a and b are not constant but change with time. In addition, a number of properties of the reflection map, including continuity and Lipschitz conditions under uniform, J 1 and M 1 metrics, are studied.

2000 AMS Mathematics Subject Classification: Primary: 60G05, 60G17; Secondary: 60J60, 60J65, 90B05, 90B22.

Keywords and phrases: Skorokhod map, Skorokhod problem, reflection map, double reflection map.

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