In mathematics, the Skorokhod integral, also named Hitsuda–Skorokhod integral, often denoted , is an operator of great importance in the theory of stochastic processes. It is named after the Ukrainian mathematician Anatoliy Skorokhod and Japanese mathematician Masuyuki Hitsuda. Part of its importance is that it unifies several concepts:
is an extension of the Itô integral to non-adapted processes;
is the adjoint of the Malliavin derivative, which is fundamental to the stochastic calculus of variations (Malliavin calculus);
is an infinite-dimensional generalization of the divergence operator from classical vector calculus.
The integral was introduced by Hitsuda in 1972[1] and by Skorokhod in 1975.[2]
^Hitsuda, Masuyuki (1972). "Formula for Brownian partial derivatives". Second Japan-USSR Symp. Probab. Th.2.: 111–114.
^Kuo, Hui-Hsiung (2014). "The Itô calculus and white noise theory: a brief survey toward general stochastic integration". Communications on Stochastic Analysis. 8 (1). doi:10.31390/cosa.8.1.07.
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