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Aspects of Stochastic Integration with Respect to Processes of Unbounded p-variation (1407.5974v3)
Published 22 Jul 2014 in math.PR
Abstract: This paper deals with stochastic integrals of form $\int_0T f(X_u)d Y_u$ in a case where the function $f$ has discontinuities, and hence the process $f(X)$ is usually of unbounded $p$-variation for every $p\geq 1$. Consequently, integration theory introduced by Young or rough path theory introduced by Lyons cannot be applied directly. In this paper we prove the existence of such integrals in a pathwise sense provided that $X$ and $Y$ have suitably regular paths together with some minor additional assumptions. In many cases of interest, our results extend the celebrated results by Young.