Skorokhod problem


In probability theory, the Skorokhod problem is the problem of solving a stochastic differential equation with a reflecting boundary condition.
The problem is named after Anatoliy Skorokhod who first published the solution to a stochastic differential equation for a reflecting Brownian motion.

Problem statement

The classic version of the problem states that given a càdlàg process and an M-matrix R, then stochastic processes and are said to solve the Skorokhod problem if for all non-negative t values,
  2. and
  3. .
The matrix R is often known as the reflection matrix, W as the reflected process and Z as the regulator process.