The Skorokhod problem is a mathematical problem in the field of stochastic processes, particularly relating to the theory of stochastic differential equations (SDEs). It involves finding a pair of processes—specifically, a continuous process and a reflecting process—that satisfy certain boundary conditions.
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Find a constrained path and a boundary regulator which together modify a given driving path. In the half-line case, write , require and nondecreasing, and require its increases to occur only where . For multidimensional orthants the regulator acts through a specified reflection matrix. The Skorokhod reflection map on the half-line solves the one-dimensional continuous-path case explicitly.