Exponential asymptotics for time–space hamiltonians
Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 4, pp. 1529-1561.

In this paper, we investigate the long time asymptotics of the exponential moment for the following time–space Hamiltonian

0 t 0 t 1 |r-s| α 0 γ(B r -B s )dsdr,t0,
where (B s ,s0) is a d-dimensional Brownian motion, the kernel γ(·): d [0,) is a homogeneous function with singularity at zero; and α 0 (0,1) together with the scaling parameter of γ satisfies certain conditions. Our work is partially motivated by the studies of the short-range sample-path intersection, the strong coupling polaron, and the parabolic Anderson models with a time–space fractional white noise potential.

Dans ce papier, nous étudions le comportement en temps long du moment exponentiel du Hamiltonien dépendant du temps

0 t 0 t 1 |r-s| α 0 γ(B r -B s )dsdr,t0,
(B s ,s0) est un mouvement brownien de dimension d, le noyau γ(·): d [0,) est une fonction homogène avec une singularité en zéro, α 0 (0,1) et le paramètre de scaling γ satisfont certaines conditions. Notre travail est partiellement motivé par l’étude des intersections ą courte portée de trajectoires, le polaron avec couplage fort et le modèle parabolique d’Anderson avec un potentiel donné par un bruit blanc fractionnaire en espace–temps.

DOI: 10.1214/13-AIHP588
Keywords: Time–space hamiltonian, brownian motion, Feynman–Kac large deviations
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Chen, Xia; Hu, Yaozhong; Song, Jian; Xing, Fei. Exponential asymptotics for time–space hamiltonians. Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 4, pp. 1529-1561. doi : 10.1214/13-AIHP588. http://www.numdam.org/articles/10.1214/13-AIHP588/

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