@article{DereudreRoelly2017,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {Path-dependent infinite-dimensional SDE with non-regular drift},
  series = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics},
  volume    = {53},
  journal   = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics},
  number    = {2},
  publisher = {Inst. of Mathematical Statistics},
  address   = {Bethesda},
  issn      = {0246-0203},
  doi       = {10.1214/15-AIHP728},
  pages     = {641 -- 657},
  year      = {2017},
  abstract  = {We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither bounded or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy and a finite second moment. The originality of our method leads in the use of the specific entropy as a tightness tool and in the description of such infinite-dimensional stochastic process as solution of a variational problem on the path space. Our result clearly improves previous ones obtained for free dynamics with bounded drift.},
  language  = {en}
}
@unpublished{DereudreRoelly2014,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {Path-dependent infinite-dimensional SDE with non-regular drift : an existence result},
  volume    = {3},
  number    = {11},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72084},
  pages     = {27},
  year      = {2014},
  abstract  = {We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.},
  language  = {en}
}