General Rough integration, Levy Rough paths and a Levy--Kintchine type formula
By Peter K. Friz, A. Shekhar. 2012
72 citations recorded by the source corpus.
We consider rough paths with jumps. In particular, the analogue of Lyons' extension theorem and rough integration are established in a jump setting, offering a pathwise view on stochastic integration against cadlag processes. A class of Levy rough paths is introduced and characterized by a sub-ellipticity condition on the left-invariant diffusion vector fields and and a certain integrability property of the Carnot--Caratheodory norm with respect to the Levy measure on the group, using Hunt's framework of Lie group valued Levy processes. Examples of Levy rough paths include standard multi-dimensional Levy process enhanced with stochastic area as constructed by D. Williams, the pure area Poisson process and Brownian motion in a magnetic field. An explicit formula for the expected signature is given.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7ef434c413601bfc99a48bfa63c363e085761c97
How researchers see this paper
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In Finance
- Peter K. Friz
- Huilin Zhang
- Ilya Chevyrev
- Terry Lyons
- Nicolas Victoir
- Samy Tindel
- Massimiliano Gubinelli
- David Nualart
In Mathematical Physics
- Ilya Chevyrev
- Peter K. Friz
- Terry Lyons
- Huilin Zhang
- Massimiliano Gubinelli
- Nicolas Victoir
- Martin Hairer
- Antoine Lejay
Citations in the corpus
- Characteristic functions of measures on geometric rough paths (2013, methodology): “Let (a,b,K) be the triplet of a Lévy process in G2(Rd) satisfying the conditions of [14] Theorem 52.”
- Differential equations driven by rough paths with jumps (2017, methodology): “6What one sees here is that our canoncial lift is the minimal jump extension [16], here in the sense that 〈X, f〉 has no jumps whenever |f | > [p].”
- Canonical RDEs and general semimartingales as rough paths (2017, methodology): “The model case of Lévy processes was studied in [41, 15].”