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math.APFeb 24, 2020
8
citations (OpenAlex)
authors
  • Carlo Bellingeri
  • Ana Djurdjevac
  • Peter K. Friz
  • Nikolas Tapia
institutions
  • Freie Universität Berlin
  • Technische Universität Berlin
  • Weierstrass Institute for Applied Analysis and Stochastics
arXiv abstractPDF
paper

Transport and continuity equations with (very) rough noise

arXiv:2002.10432 · doi:10.1007/s42985-021-00101-y

Abstract

Existence and uniqueness for rough flows, transport and continuity equations driven by general geometric rough paths are established.

arXiv comment20 pages

References in corpus (6)

  • Well-posedness of the transport equation by stochastic perturbation
  • Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness
  • A construction of the rough path above fractional Brownian motion using Volterra's representation
  • Stochastic partial differential equations: a rough path view
  • The density of the solution to the stochastic transport equation with fractional noise
  • Partial differential equations driven by rough paths

Cited by in corpus (2)

  • Quasi-geometric rough paths and rough change of variable formula
  • Scaling Limits of Stochastic Transport Equations on Manifolds
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