Acta Applicandae Mathematicae

, Volume 151, Issue 1, pp 81–88 | Cite as

Stochastic Quantization for the Fractional Edwards Measure

  • Wolfgang BockEmail author
  • Torben Fattler
  • Ludwig Streit


We prove that there exists a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion, \(\mu_{ {g,H}}\), \(H\in (0,1)\) for \(dH < 1\). The diffusion is constructed in the framework of Dirichlet forms in infinite dimensional (Gaussian) analysis. Moreover, the process is invariant under time translations.


Stochastic quantization Edwards model Fractional Brownian motion Dirichlet forms White noise analysis 



We truly thank M. Röckner for helpful discussions. Furthermore we thank M. Grothaus and M. J. Oliveira for helpful comments. Moreover, the authors are grateful for the referee’s constructive comments. Financial support by CRC 701 and the mathematics department of the University of Kaiserslautern for research visits at Bielefeld university are gratefully acknowledged.


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Technomathematics GroupUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Functional Analysis and Stochastic Analysis GroupUniversity of KaiserslauternKaiserslauternGermany
  3. 3.BIBOSBielefeldGermany
  4. 4.CIMA-UMAFunchalPortugal

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