Skorokhod problem

The classic version of the problem states^[5] that given a càdlàg process {X(t), t ≥ 0} and an M-matrix R, then stochastic processes {W(t), t ≥ 0} and {Z(t), t ≥ 0} are said to solve the Skorokhod problem if for all non-negative t values,

1. ${\displaystyle W(t)=X(t)+RZ(t)\geq 0}$
2. ${\displaystyle Z(0)=0}$ and ${\displaystyle dZ(t)\geq 0}$
3. ${\displaystyle \int _{0}^{t}W_{i}(s){\text{d}}Z_{i}(s)=0}$.

The matrix R is often known as the reflection matrix, W(t) as the reflected process and Z(t) as the regulator process.

• List of things named after Anatoliy Skorokhod