Rough path
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In stochastic analysis, a rough path is an analytical and algebraic object associated to an irregular path allowing one to define and study solutions to differential equations controlled by such irregular paths, for example a Wiener process. The theory was developed in the 1990s by Terry Lyons.[1][2][3] Several accounts of the theory are available.[4][5][6][7] Martin Hairer used rough paths to solve the KPZ equation.[8] He then proposed a significant generalization known as the theory of regularity structures.[9] For this work he was awarded a Fields medal in 2014 .
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