In probability theory, the Skorokhod problem is the problem of solving a stochastic differential equation with a reflecting boundary condition.
[1] The problem is named after Anatoliy Skorokhod who first published the solution to a stochastic differential equation for a reflecting Brownian motion.
[2][3][4] 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, The matrix R is often known as the reflection matrix, W(t) as the reflected process and Z(t) as the regulator process.
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