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Stochastic Quantization for the Fractional Edwards Measure

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Technomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Wolfgang Bock

  2. Functional Analysis and Stochastic Analysis Group, University of Kaiserslautern, Kaiserslautern, Germany

    Torben Fattler

  3. BIBOS, Bielefeld, Germany

    Ludwig Streit

  4. CIMA-UMA, Funchal, Portugal

    Ludwig Streit

Authors
  1. Wolfgang Bock
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  2. Torben Fattler
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  3. Ludwig Streit
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Correspondence to Wolfgang Bock.

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Bock, W., Fattler, T. & Streit, L. Stochastic Quantization for the Fractional Edwards Measure. Acta Appl Math 151, 81–88 (2017). https://doi.org/10.1007/s10440-017-0103-8

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  • DOI: https://doi.org/10.1007/s10440-017-0103-8

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