The \(p\)-variation and an extension of the class of semimartingales (Q1415506)

Dudley, Norvaiša and Lyons proved that results concerning integral equations cannot be extended to functions with bounded 2-variation, while they are valid for functions of \(p\)-variation for some \(p<2\). The paper discusses the possibility of incorporating such results into the stochastic analysis, more precisely by replacing the bounded variation component of a semimartingale by a stochastic process having almost all sample functions of bounded \(p\)-variation for some \(p<2\).