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Partial differential equations driven by rough paths
16 references·5 citing·30 second hop
Partial differential equations driven by rough paths (2009)Partial differential equations driven by …Multidimensional Stochastic Processes as Rough Paths (2010)Multidimensional Stochastic P…Differential equations driven by Gaussian signals (2010)Differential equations driven…The 1-d stochastic wave equation driven by a fractional Brownian sheet (2007)The 1-d stochastic wave equat…Differential Equations Driven by Rough Paths (2007)Differential Equations Driven…Differential Equations Driven by Rough Paths (2007)Differential Equations Driven…Young Integrals and SPDEs (2006)Young Integrals and SPDEsRough evolution equations (2006)Rough evolution equationsA note on the notion of geometric rough paths (2005)A note on the notion of geome…Approximations of the Brownian rough path with applications to stochastic analysis (2004)Approximations of the Brownia…System Control and Rough Paths (2002)System Control and Rough PathsStochastic Flows and Stochastic Differential Equations (1998)Stochastic Flows and Stochast…Differential equations driven by rough signals (1998)Differential equations driven…Almost sure approximation of Wong-Zakai type for stochastic partial differential equations (1995)Almost sure approximation of …Stochastic Differential Equations and Diffusion Processes (1983)Stochastic Differential Equat…Stochastic partial differential equations and filtering of diffusion processes (1980)Stochastic partial differenti…MULTI-DIMENSIONAL DIFFUSION PROCESSES (1980)MULTI-DIMENSIONAL DIFFUSION P…A priori estimates for rough PDEs with application to rough conservation laws (2019)A priori estimates for rough …Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac (2017)Stochastic partial differenti…Backward stochastic differential equations with rough drivers (2012)Backward stochastic different…Malliavin Calculus for Fractional Delay Equations (2011)Malliavin Calculus for Fracti…ANOTHER APPROACH TO SOME ROUGH AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS (2011)ANOTHER APPROACH TO SOME ROUG…The Malliavin Calculus and Related Topics (1995)An introduction to stochastic partial differential equations (2006)Delay equations driven by rough paths (2008)Non-linear rough heat equations (2011)Integration with respect to fractal functions and stochastic calculus. I (1998)Stochastic analysis, rough path analysis and fractional Brownian motions (2002)Smoothness of the density for solutions to Gaussian rough differential equations (2014)The signature of a rough path: Uniqueness (2016)Analysis of the Rosenblatt process (2008)Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation (2008)Stochastic heat equation driven by fractional noise and local time (2008)Differential equations driven by fractional Brownian motion (2002)Controlling rough paths (2004)Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation (1992)Backward Stochastic Differential Equations in Finance (1997)Controlled Markov Processes and Viscosity Solutions (2005)Optimal Control for Partially Observed Diffusions (1982)Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions (1983)Backward doubly stochastic differential equations and systems of quasilinear SPDEs (1994)An Overview of Value at Risk (1997)Pricing the risks of default (1998)Robustness of the Black and Scholes Formula (1998)ARCH models as diffusion approximations (1990)Chapter 49 Arch models (1994)5 Stochastic volatility (1996)UNIQUENESS FOR THE SIGNATURE OF A PATH OF BOUNDED VARIATION AND THE REDUCED PATH GROUP (2006)Uniqueness for the signature of a path of bounded variation and the reduced path group (2010)A Wong-Zakai theorem for stochastic PDEs (2015)Densities for rough differential equations under Hörmander’s condition (2010)Averaging along irregular curves and regularisation of ODEs (2016)
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References

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  • 1980MULTI-DIMENSIONAL DIFFUSION PROCESSES1,243 cited
  • 1998Stochastic Flows and Stochastic Differential Equations1,182 cited
  • 1998Differential equations driven by rough signals1,077 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
  • 2007Differential Equations Driven by Rough Paths237 cited
  • 2006Rough evolution equations120 cited
  • 2010Differential equations driven by Gaussian signals113 cited
  • 2006Young Integrals and SPDEs100 cited
  • 1995Almost sure approximation of Wong-Zakai type for stochastic partial differential equations81 cited
  • 2004Approximations of the Brownian rough path with applications to stochastic analysis65 cited
  • 2007The 1-d stochastic wave equation driven by a fractional Brownian sheet62 cited
  • 2005A note on the notion of geometric rough paths

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60 cited

Cited by

  • 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
  • 2011ANOTHER APPROACH TO SOME ROUGH AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS28 cited