An analytic approach to infinite-dimensional continuity and Fokker-Planck-Kolmogorov equations

• Vladimir I. Bogachev ^[1] ; Giuseppe Da Prato ^[2] ; Michael Röckner ^[3] ; Stanislav V. Shaposhnikov ^[1]
  1. [1] Moscow State University

     Moscow State University

     Rusia

     
  2. [2] Scuola Normale Superiore di Pisa, Italy
  3. [3] Universit¨at Bielefeld, Germany

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 3, 2015, págs. 983-1023
• Idioma: inglés
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• Resumen

  • We prove a new uniqueness result for solutions to Fokker-Planck- Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider infinite-dimensional drifts that admit certain finite-dimensional approximations. In contrast to much of the previous work on FPK-equations in infinite dimensions, we include cases with non-constant coefficients in the second order part and also include degenerate cases where these coefficients can even be zero. A new existence result is also proved. Some applications to FPK equations associated with SPDE’s are presented.