LÉVY AREA OF WIENER PROCESSES IN BANACH SPACES

By Michel Ledoux, Terry Lyons, Zhongmin Qian. 2002

74 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/421e35820dcca0756b2fea8d4b5e8fb8889543ff

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In Applied Mathematics

In Finance

Citations in the corpus

Stochastic analysis, rough path analysis and fractional Brownian motions (2002, methodology): “More recently, it has been used to construct canonical geometric rough paths associated to a class of Markovian processes [BHL], [HL1], and Brownian motions in Banach spaces [ LLQ ].”
General Rough integration, Levy Rough paths and a Levy--Kintchine type formula (2012, methodology): “[23, 12, 30] (i) As in whenever γ > p− 1 > 0, with tk = k2T , one has (2.”
Discretely sampled signals and the rough Hoff process (2013, methodology): “tion of a level-2 rough path by a weighted sum of its moments and areas over every dyadic interval in [0,1] could be used. For more details on this trick we refer the reader to its ﬁrst appearance in [15] by Ledoux et al.11 This was attempted! However, this technique enforces restrictions on the rat”
Young Integrals and SPDEs (2004, background): “On the other hand, some di�erential equations in a Banach space, driven by a rough path, are considered in ( LLQ02 ), but the question of the regularization of the noise by a semi-group is not addressed in that last reference.”
An extension theorem to rough paths (2007, background): ““Canonical” lifts have been constructed for Brownian motion [13,10], fractional Brownian motion with Hurst parameter greater than 1/4 [3,13], free Brownian motion [2,18], and a large class of random paths on fractals [1,8].”
An Introduction to Rough Paths (2003, background): “See also [47] for an example of use of the Poincaré-Birkhoff-Witt Theorem that gives a basis of Lie algebras.”
Yet another introduction to rough paths (2009, background): “Finally, note that the theory of rough paths may also be applied to the infinite dimensional case (see [LLQ02] for example).”
Semi-martingales and rough paths theory (2005, methodology): “Although the rough path theory is completely deterministic, it has been used for a large class of processes, including Brownian motion, some Gaussian processes in a Banach space [18], fractional Brownian motion [5], free Brownian motion [3], symmetric Markov process [1],.”
Large deviations for rough paths of the fractional Brownian motion (2004, methodology): “Indeed, linear interpolations of interesting examples like Brownian motion, B-valued Wiener process, free Brownian motion and fractional Brownian motion have been successfully used to define the corresponding geometric rough path (see [15], [11], [3], [4], respectively).”