Construction of an Edwards’ probability measure on $\mathcal{C}(\mathbb{R}_{+},\mathbb{R})$

Najnudel, Joseph

Ann. Probab., Tome 38 (2010) no. 1, p. 2295-2321 / Harvested from Project Euclid

Résumé

In this article, we prove that the measures ℚ_T associated to the one-dimensional Edwards’ model on the interval [0, T] converge to a limit measure ℚ when T goes to infinity, in the following sense: for all s≥0 and for all events Λ_s depending on the canonical process only up to time s, ℚ_T(Λ_s) → ℚ(Λ_s). ¶ Moreover, we prove that, if ℙ is Wiener measure, there exists a martingale (D_s)_s∈ℝ₊ such that $\mathbb{Q}(\Lambda_{s})=\mathbb{E}_{\mathbb{P}}(\mathbh{1}_{\Lambda_{s}}D_{s})$ , and we give an explicit expression for this martingale.

Publié le : 2010-11-15
Classification: Edwards’ model, polymer measure, Brownian motion, penalization, local time, 60F99, 60G30, 60G44, 60H10, 60J65

@article{1285334207,
     author = {Najnudel, Joseph},
     title = {Construction of an Edwards' probability measure on $\mathcal{C}(\mathbb{R}\_{+},\mathbb{R})$},
     journal = {Ann. Probab.},
     volume = {38},
     number = {1},
     year = {2010},
     pages = { 2295-2321},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285334207}
}

Najnudel, Joseph. Construction of an Edwards’ probability measure on $\mathcal{C}(\mathbb{R}_{+},\mathbb{R})$. Ann. Probab., Tome 38 (2010) no. 1, pp.  2295-2321. http://gdmltest.u-ga.fr/item/1285334207/