Multidimensional Stochastic Processes as Rough Paths: Variation and Hölder spaces on free groups

By Peter K. Friz, Nicolas Victoir. 2010

210 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7479b9a2acbbdf958c9d17a414ec88a6bef67b3

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Citations in the corpus

Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion (2009, methodology): “Although the basic theory of SDEs driven by fBm (for H ∈ (1/4,1)) is now well established (see, for example, [6, 10,24,31]), the ergodicity of such SDEs has only been studied recently.”
Integrability of (Non-)Linear Rough Differential Equations and Integrals (2011, background): “For the lower bound, recall that from [12], Theorem 15.”
Yet another introduction to rough paths (2009, background): “The book [FV06a] contains a large number of these constructions).”
Flows driven by rough paths (2012, background): “It follows in particular from this well-posedness result that there is no explosion, which generalizes to our infinite dimensional setting the corresponding results of [10] and [16], which only treat the case 2 6 p 3 without a drift, and the finite dimensional analogue result of Friz-Victoir [4], ”
Convergence rates for the full Gaussian rough paths (2011, background): “[4], [9]) shows that the step-N Euler scheme(3) for an RDE driven by a 1/p-Hölder rough path with step size 1/k (i.”
The Signature of a Rough Path: Uniqueness (2014, background): “26 in [14] for the existence of such sequence).”
Pathwise solutions of SPDEs driven by Hölder-continuous integrators with exponent larger than $1/2$ and random dynamical systems (2013, methodology): “One of these attempts is given by the Rough Path Theory, and we refer to the monographs by Lyons and Qian [16] and Friz and Victoir [5] for a comprehensive presentation of this theory.”
A stochastic sewing lemma and applications (2018, result): “As in Lyons’ rough path theory ([32, 16]), we expect that such an extension is necessary to enlarge the scope of applications of the stochastic sewing lemma and possibly improve some of the results stated in the current paper.”
Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations (2011, background): “, [16] and the references therein; the third component is precisely Lévy’s stochastic area.”