Construction of an Edwards’ probability measure on $\mathcal{C}(\mathbb{R}_{+},\mathbb{R})$
Year: 2010
Type: article
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, ℚT(Λs) → 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.
Source: The Annals of Probability
DOI: 10.1214/10-aop540
Author: Joseph Najnudel
Institution: University of Zurich
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2083489402