An explicit formula for the Skorokhod map on [0,a].
An explicit formula for the Skorokhod map on [0,a].
复制标题
[0,a] 上 Skorokhod 映射的显式公式。
DOI：
10.1214/009117906000000890
复制
发表时间：
2007
影响因子：
2.3
通讯作者：
S. Shreve
中科院分区：
文献类型：
--
作者：
Łukasz Kruk;J. Lehoczky;K. Ramanan;S. Shreve
Skorokhod映射是构造具有反射边界条件的随机微分方程的解的一个方便的工具。本文导出了[0，a]上Skorokhod映射Γ 0，a的一个显式公式.具体地说，证明了在具有左极限取值于R的右连续函数空间D[0，∞）上，Γ 0，a = Λ a o Γ 0，其中Λ a：D[0，∞）→ D[0，∞）定义为Λ a（Φ）（t）= Φ（t）- sups∈[0，t] [（Φ（s）-a）+ Λ infu∈[s，t] Φ（u）]和Γ 0：D[0，∞）→ D[0，∞）是[0，∞）上的Skorokhod映射，它由下式给出：Γ 0（t）（t）= ∞（t）+ sup s∈[0，t] [-∞（s）] + .此外，还发展了Λ a的性质，建立了Γ 0，a的比较性质.
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 Γ 0,a on [0, a] for any a > 0 is derived. Specifically, it is shown that on the space D[0, ∞) of right-continuous functions with left limits taking values in R, Γ 0,a = Λ a o Γ 0 , where Λ a : D[0, ∞) → D[0, ∞) is defined by Λ a (Φ) (t) = Φ(t)- sups∈[0,t] [(Φ(s)-a) + Λ infu∈[s,t] Φ(u)] and Γ 0 :D[0, ∞) → D[0, ∞) is the Skorokhod map on [0, ∞), which is given explicitly by Γ 0 (ψ)(t) = ψ(t) + sup s∈[0,t] [-ψ(s)] + . In addition, properties of Λ a are developed and comparison properties of Γ 0,a are established.