An explicit formula for the Skorokhod map on [0, a]
成果类型：
Article
署名作者：
Kruk, Lukasz; Lehoczky, John; Ramanan, Kavita; Shreve, Steven
署名单位：
Maria Curie-Sklodowska University; Carnegie Mellon University; Carnegie Mellon University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117906000000890
发表日期：
2007
页码：
1740-1768
关键词：
摘要：
The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map Gamma(0,a) on [0,a] for any a > 0 is derived. Specifically, it is shown that on the space D[0, infinity) of right-continuous functions with left limits taking values in R, Gamma (0, a) = Lambda(a) omicron Gamma(0), where Lambda(a) : D[0, infinity) -> D [0, infinity) is defined by [Graphics] and Gamma(0): D[O, infinity) ->. D[O, infinity) is the Skorokhod map on [0, infinity), which is given explicitly by [Graphics] In addition, properties of Lambda(a) are developed and comparision properites of Gamma(0,a) are established.