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A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations
16 references·0 citing·35 second hop
A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations (2014)A Lévy area between Brownian motion and r…Integrability and tail estimates for Gaussian rough differential equations (2013)Integrability and tail estima…Non-linear rough heat equations (2011)Non-linear rough heat equatio…Differential equations driven by Gaussian signals (2010)Differential equations driven…A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2010)A (rough) pathwise approach t…Rough path limits of the Wong–Zakai type with a modified drift term (2009)Rough path limits of the Wong…Partial differential equations driven by rough paths (2009)Partial differential equation…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 SPDEsAn extension theorem to rough paths (2006)An extension theorem to rough…Backward stochastic differential equations and quasilinear parabolic partial differential equations (2005)Backward stochastic different…A note on the notion of geometric rough paths (2005)A note on the notion of geome…Controlling rough paths (2004)Controlling rough pathsSystem Control and Rough Paths (2002)System Control and Rough PathsDifferential equations driven by rough signals (1998)Differential equations driven…Stochastic Partial Differential Equations and Their Applications (1992)Stochastic Partial Differenti…Integration with respect to fractal functions and stochastic calculus. I (1998)An introduction to stochastic partial differential equations (2006)The 1-d stochastic wave equation driven by a fractional Brownian sheet (2007)Pathwise solutions of SPDEs driven by Hölder-continuous integrators with exponent larger than $1/2$ and random dynamical systems (2013)Brownian Motion and Stochastic Calculus (1988)Adapted solution of a backward stochastic differential equation (1990)Solving forward-backward stochastic differential equations explicitly — a four step scheme (1994)Reflected solutions of backward SDE's, and related obstacle problems for PDE's (1997)Backward stochastic differential equations and partial differential equations with quadratic growth (2000)Brownian Motion and Stochastic Calculus (2007)Stochastic Differential Equations and Diffusion Processes (1983)Continuous Martingales and Brownian Motion (1999)The Malliavin Calculus and Related Topics (2006)Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths (2013)Smoothness of the density for solutions to Gaussian rough differential equations (2014)Stochastic Flows and Stochastic Differential Equations (1998)Controlled Markov Processes and Viscosity Solutions (2005)Rough Burgers-like equations with multiplicative noise (2011)A priori estimates for rough PDEs with application to rough conservation laws (2019)Stochastic analysis, rough path analysis and fractional Brownian motions (2002)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)Multidimensional Stochastic Processes as Rough Paths (2010)Elements of Stochastic Calculus via Regularization (2007)Ramification of rough paths (2009)Averaging along irregular curves and regularisation of ODEs (2016)Equations différentielles stochastiques rétrogrades réfléchies dans un convexe (1996)Stability of BSDEs with Random Terminal Time and Homogenization of Semilinear Elliptic PDEs (1998)Reflected backward stochastic differential equation with jumps and RCLL obstacle (2008)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)
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References

  • 1998Differential equations driven by rough signals1,077 cited
  • 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations782 cited
  • 2004Controlling rough paths578 cited
  • 2002System Control and Rough Paths519 cited
  • 2007Differential Equations Driven by Rough Paths381 cited
  • 2007Differential Equations Driven by Rough Paths237 cited
  • 1992Stochastic Partial Differential Equations and Their Applications126 cited
  • 2010Differential equations driven by Gaussian signals113 cited
  • 2006Young Integrals and SPDEs100 cited
  • 2010A (rough) pathwise approach to a class of non-linear stochastic partial differential equations90 cited
  • 2013Integrability and tail estimates for Gaussian rough differential equations85 cited
  • 2006An extension theorem to rough paths84 cited
  • 2011Non-linear rough heat equations73 cited
  • 2005A note on the notion of geometric rough paths60 cited
  • 2009Partial differential equations driven by rough paths56 cited
  • 2009Rough path limits of the Wong–Zakai type with a modified drift term

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