Rough Path Analysis Via Fractional Calculus

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dc.creatorHu, Yaozhong
dc.creatorNualart, David
dc.date2006-02-02
dc.date.accessioned2026-07-07T07:03:04Z
dc.date.available2026-07-07T07:03:04Z
dc.descriptionUsing fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued Hölder continuous functions of order $\displaystyle β\in (\frac13, \frac12)$ and $f$ is a continuously differentiable function such that $f'$ is $λ$-Höldr continuous for some $λ>\frac1β-2$. Under some further smooth conditions on $f$ the integral is a continuous functional of $x$, $y$, and the tensor product $x\otimes y$ with respect to the Hölder norms. We derive some estimates for these integrals and we solve differential equations driven by the function $y$. We discuss some applications to stochastic integrals and stochastic differential equations.
dc.identifierhttps://arxiv.org/abs/math/0602050
dc.identifierhttp://arxiv.org/abs/math/0602050
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/108833
dc.subjectProbability
dc.subjectDynamical Systems
dc.subject60H10, 26a33
dc.titleRough Path Analysis Via Fractional Calculus
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