Continuous differentiability of renormalized intersection local times in R 1
Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 4, p. 1025-1041

We study γk(x2, …, xk; t), the k-fold renormalized self-intersection local time for brownian motion in R1. Our main result says that γk(x2, …, xk; t) is continuously differentiable in the spatial variables, with probability 1.

Nous étudions γk(x2, …, xk; t), le temps local renormalisé d'auto-intersection d'ordre k du mouvement brownien dans R1. Notre résultat principal montre que γk(x2, …, xk; t) est presque sûrement continûment différentiable dans les variables spatiales.

DOI : https://doi.org/10.1214/09-AIHP338
Classification:  60J55,  60J65
Keywords: continuous differentiability, intersection local time, brownian motion
@article{AIHPB_2010__46_4_1025_0,
     author = {Rosen, Jay S.},
     title = {Continuous differentiability of renormalized intersection local times in $R^1$},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {4},
     year = {2010},
     pages = {1025-1041},
     doi = {10.1214/09-AIHP338},
     zbl = {1210.60084},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2010__46_4_1025_0}
}
Rosen, Jay S. Continuous differentiability of renormalized intersection local times in $R^1$. Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 4, pp. 1025-1041. doi : 10.1214/09-AIHP338. http://www.numdam.org/item/AIHPB_2010__46_4_1025_0/

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