The play operator,the truncated variation and the generalisation of the Jordan decomposition |
| |
| Authors: | R Łochowski R Ghomrasni |
| |
| Institution: | 1. Department of Mathematics and Mathematical Economics, Warsaw School of Economics, Madalińskiego 6/8, 02‐513 Warszawa, Poland;2. Department of Core Mathematics and Social Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia;3. Department of Mathematical Sciences, University of Stellenbosch, Stellenbosch 7602, South Africa;4. The African Institute for Mathematical Sciences, 6‐8 Melrose Road, Muizenberg 7945, South Africa |
| |
| Abstract: | The play operator minimalizes the total variation on intervals, 0,T],T > 0, of functions approximating uniformly given regulated function with given accuracy and starting from a given point. In this article, we link the play operator with the so‐called truncated variation functionals, introduced recently by the second‐named author, and provide a semi‐explicit expression for the play operator in terms of these functionals. Generalisation for time‐dependent boundaries is also considered. This gives the best possible lower bounds for the total variation of the outputs of the play operator and its Jordan‐like decomposition. Copyright © 2014 John Wiley & Sons, Ltd. |
| |
| Keywords: | play operator truncated variation continuity of the play operator rate independence the Skorohod problem |
|
|
