Differential equations driven by gaussian signals
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 2, p. 369-413
Nous donnons une condition simple et optimale sur la covariance d'un processus gaussien pour que celui-ci puisse être associé naturellement à un rough path. Une fois ce processus construit, nous démontrons un principe de grandes déviations, un théorème du support, et plusieurs résultats d'approximations. Avec la théorie des rough paths de T. Lyons, nous obtenons ainsi un cadre puissant, bien que conceptuellement simple, dans lequel nous pouvons analyser les équations différentielles conduites par des signaux gaussiens dans le sens des rough paths.
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.
@article{AIHPB_2010__46_2_369_0,
     author = {Friz, Peter and Victoir, Nicolas},
     title = {Differential equations driven by gaussian signals},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {2},
     year = {2010},
     pages = {369-413},
     doi = {10.1214/09-AIHP202},
     zbl = {1202.60058},
     mrnumber = {2667703},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2010__46_2_369_0}
}
Friz, Peter; Victoir, Nicolas. Differential equations driven by gaussian signals. Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 2, pp. 369-413. doi : 10.1214/09-AIHP202. http://www.numdam.org/item/AIHPB_2010__46_2_369_0/

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