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Absolute Continuity of the Invariant Measures for Some Stochastic PDEs

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Abstract

We consider a free system and an interacting systems having invariant measures μ and ν respectively. Under suitable assumptions we prove an explicit formula relating ν with μ and implying the absolute continuity of ν with respect to μ. We apply our result to a reaction-diffusion equation and to the Burgers equation.

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Authors and Affiliations

  1. Scuola Normale Superiore di Pisa, Piazza dei Cavalieri7, 56126, Pisa, Italy

    Giuseppe Da Prato

  2. École Normale Supérieure de Cachan, antenne de Bretagne, Campus de Ker Lann, 35170, Bruz, France

    Arnaud Debussche

Authors
  1. Giuseppe Da Prato
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  2. Arnaud Debussche
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Da Prato, G., Debussche, A. Absolute Continuity of the Invariant Measures for Some Stochastic PDEs. Journal of Statistical Physics 115, 451–468 (2004). https://doi.org/10.1023/B:JOSS.0000019816.42914.19

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  • DOI: https://doi.org/10.1023/B:JOSS.0000019816.42914.19

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