Explicit solutions of the extended Skorokhod problems in affine transformations of time-dependent strata
type: Item
instance of: scholarly article
title: Explicit solutions of the extended Skorokhod problems in affine transformations of time-dependent strata
zbMATH Open document ID: 1470.60165
DOI: 10.1155/2021/9992546
author: Marek Slaby
published in: Journal of Probability and Statistics
publication date: 2021-08-26T00:00:00Z
review text: Summary: The goal of this paper is to expand the explicit formula for the solutions of the extended Skorokhod problem developed earlier for a special class of constraining domains in \(\mathbb{R}^n\) with orthogonal reflection fields. We examine how affine transformations convert solutions of the extended Skorokhod problem into solutions of the new problem for the transformed constraining system. We obtain an explicit formula for the solutions of the extended Skorokhod problem for any \(\mathbb{R}^n\)- valued càdlàg function with the constraining set that changes in time and the reflection field naturally defined by any basis. The evolving constraining set is a region sandwiched between two graphs in the coordinate system generating the reflection field. We discuss the Lipschitz properties of the extended Skorokhod map and derive Lipschitz constants in special cases of constraining sets of this type.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 7385430
zbMATH Keywords: extended Skorokhod problem
zbMATH Keywords: Skorokhod map
zbMATH Keywords: Lipschitz constants
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/9992546
OpenAlex ID: W3176319030
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description: scientific article; zbMATH DE number 7385430