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arxiv: 1807.07358 · v1 · pith:N5GWMZUZnew · submitted 2018-07-19 · 🧮 math-ph · math.MP· math.PR

Stochastic Quantization for the Edwards Measure of Fractional Brownian Motion with Hd=1

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keywords fractionalmeasurebrownianedwardsmotioncasecorrespondingalong
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In this paper we construct a Markov process which has as invariant measure the fractional Edwards measure based on a $d$-dimensional fractional Brownian motion, with Hurst index $H$ in the case of $Hd=1$. We use the theory of classical Dirichlet forms. However since the corresponding self-intersection local time of fractional Brownian motion is not Meyer-Watanabe differentiable in this case, we show the closability of the form via quasi translation invariance of the fractional Edwards measure along shifts in the corresponding fractional Cameron-Martin space.

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