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A (rough) pathwise approach to a class of non-linear stochastic partial differential equations
15 references·11 citing·33 second hop
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this work references cited by second hop

References

  • 2005Controlled Markov Processes and Viscosity Solutions2,698 cited
  • 2006The Malliavin Calculus and Related Topics2,470 cited
  • 1998Stochastic Flows and Stochastic Differential Equations1,182 cited
  • 1998Differential equations driven by rough signals1,077 cited
  • 2000Backward stochastic differential equations and partial differential equations with quadratic growth763 cited
  • 2010Multidimensional Stochastic Processes as Rough Paths750 cited
  • 1980Stochastic partial differential equations and filtering of diffusion processes576 cited
  • 2002System Control and Rough Paths519 cited
  • 2007Differential Equations Driven by Rough Paths381 cited
  • 1994Backward doubly stochastic differential equations and systems of quasilinear SPDEs337 cited
  • 2002Stochastic analysis, rough path analysis and fractional Brownian motions317 cited
  • 2007Differential Equations Driven by Rough Paths237 cited
  • 2010Differential equations driven by Gaussian signals113 cited
  • 2001Stochastic viscosity solutions for nonlinear stochastic partial differential equations. Part I107 cited
  • 2002Large deviations and support theorem for diffusion processes via rough paths101 cited

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Cited by

  • 2011Non-linear rough heat equations73 cited
  • 2011Rough Burgers-like equations with multiplicative noise59 cited
  • 2019A priori estimates for rough PDEs with application to rough conservation laws53 cited
  • 2012Backward stochastic differential equations with rough drivers34 cited
  • 2011Malliavin Calculus for Fractional Delay Equations33 cited
  • 2017Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac29 cited
  • 2016On a class of stochastic partial differential equations27 cited
  • 2015Local pathwise solutions to stochastic evolution equations driven by fractional Brownian motions with Hurst parameters $H\in (1/3,1/2]$27 cited
  • 2015Stochastic scalar conservation laws driven by rough paths26 cited
  • 2014A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations26 cited
  • 2016Rough linear transport equation with an irregular drift26 cited