Differential equations driven by gaussian signals

Peter Friz; Nicolas Victoir

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 2, page 369-413
  • ISSN: 0246-0203

Abstract

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We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.

How to cite

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Friz, Peter, and Victoir, Nicolas. "Differential equations driven by gaussian signals." Annales de l'I.H.P. Probabilités et statistiques 46.2 (2010): 369-413. <http://eudml.org/doc/241550>.

@article{Friz2010,
abstract = {We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.},
author = {Friz, Peter, Victoir, Nicolas},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {rough paths; gaussian processes; Gaussian processes},
language = {eng},
number = {2},
pages = {369-413},
publisher = {Gauthier-Villars},
title = {Differential equations driven by gaussian signals},
url = {http://eudml.org/doc/241550},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Friz, Peter
AU - Victoir, Nicolas
TI - Differential equations driven by gaussian signals
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 2
SP - 369
EP - 413
AB - We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.
LA - eng
KW - rough paths; gaussian processes; Gaussian processes
UR - http://eudml.org/doc/241550
ER -

References

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