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November 2010 Construction of an Edwards’ probability measure on $\mathcal{C}(\mathbb{R}_{+},\mathbb{R})$
Joseph Najnudel
Ann. Probab. 38(6): 2295-2321 (November 2010). DOI: 10.1214/10-AOP540

Abstract

In this article, we prove that the measures ℚT 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 Λs depending on the canonical process only up to time s, ℚTs) → ℚ(Λs).

Moreover, we prove that, if ℙ is Wiener measure, there exists a martingale (Ds)s∈ℝ+ such that $\mathbb{Q}(\Lambda_{s})=\mathbb{E}_{\mathbb{P}}(𝟙 _{\Lambda_{s}}D_{s})$, and we give an explicit expression for this martingale.

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Joseph Najnudel. "Construction of an Edwards’ probability measure on $\mathcal{C}(\mathbb{R}_{+},\mathbb{R})$." Ann. Probab. 38 (6) 2295 - 2321, November 2010. https://doi.org/10.1214/10-AOP540

Information

Published: November 2010
First available in Project Euclid: 24 September 2010

zbMATH: 1234.60038
MathSciNet: MR2683631
Digital Object Identifier: 10.1214/10-AOP540

Subjects:
Primary: 60F99 , 60G30 , 60G44 , 60H10 , 60J65

Keywords: Brownian motion , Edwards’ model , Local time , Penalization , polymer measure

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 6 • November 2010
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