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.
Citation
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
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