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Differential Equations Driven by Rough Paths
4 references·16 citing·36 second hop
Differential Equations Driven by Rough Paths (2007)Differential Equations Driven by Rough Pa…Realized power variation and stochastic volatility models (2003)Realized power variation and …Stochastic analysis, rough path analysis and fractional Brownian motions (2002)Stochastic analysis, rough pa…Integration with respect to fractal functions and stochastic calculus. I (1998)Integration with respect to f…Differential equations driven by rough signals (1998)Differential equations driven…Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU (2020)Signatory: differentiable com…Differential equations driven by rough paths with jumps (2018)Differential equations driven…A stochastic sewing lemma and applications (2018)A stochastic sewing lemma and…The signature of a rough path: Uniqueness (2016)The signature of a rough path…The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory (2016)The Jain–Monrad criterion for…Rough paths and 1d SDE with a time dependent distributional drift: application to polymers (2015)Rough paths and 1d SDE with a…Flows driven by rough paths (2015)Flows driven by rough pathsSmoothness of the density for solutions to Gaussian rough differential equations (2014)Smoothness of the density for…Rough paths, Signatures and the modelling of functions on streams (2014)Rough paths, Signatures and t…Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths (2013)Regularity of laws and ergodi…Rough Burgers-like equations with multiplicative noise (2011)Rough Burgers-like equations …Controlled differential equations as Young integrals: A simple approach (2010)Controlled differential equat…A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2010)A (rough) pathwise approach t…Partial differential equations driven by rough paths (2009)Partial differential equation…Rough path analysis via fractional calculus (2008)Rough path analysis via fract…UNIQUENESS FOR THE SIGNATURE OF A PATH OF BOUNDED VARIATION AND THE REDUCED PATH GROUP (2006)UNIQUENESS FOR THE SIGNATURE …Stochastic Differential Equations and Diffusion Processes (1983)Continuous Martingales and Brownian Motion (1999)Stochastic integration with respect to fractional brownian motion (2003)On bifractional Brownian motion (2005)Brownian Motion and Stochastic Calculus (2007)Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008)Multiple Wiener Integral (1951)Fractional Brownian Motions, Fractional Noises and Applications (1968)Integration questions related to fractional Brownian motion (2000)Stochastic Calculus with Respect to Gaussian Processes (2001)Differential equations driven by fractional Brownian motion (2002)The Pricing of Options on Assets with Stochastic Volatilities (1987)Why Does Stock Market Volatility Change Over Time? (1989)A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993)Limit theorems for multipower variation in the presence of jumps (2006)Realized jumps on financial markets and predicting credit spreads (2010)Volatility Jumps (2010)The Malliavin Calculus and Related Topics (2006)Integrability and tail estimates for Gaussian rough differential equations (2013)From Rough Path Estimates to Multilevel Monte Carlo (2016)Multidimensional Stochastic Processes as Rough Paths (2010)Geometric versus non-geometric rough paths (2015)Physical Brownian motion in a magnetic field as a rough path (2015)Stochastic Flows and Stochastic Differential Equations (1998)Controlled Markov Processes and Viscosity Solutions (2005)Non-linear rough heat equations (2011)A priori estimates for rough PDEs with application to rough conservation laws (2019)System Control and Rough Paths (2002)Characteristic functions of measures on geometric rough paths (2016)General rough integration, Lévy rough paths and a Lévy–Kintchine-type formula (2017)A Data-Driven Market Simulator for Small Data Environments (2020)Differential Equations Driven by Rough Paths (2007)Controlling rough paths (2004)Approximation of SDEs: a stochastic sewing approach (2021)C∞− regularization of ODEs perturbed by noise (2021)Distribution dependent SDEs driven by additive fractional Brownian motion (2022)
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References

  • 1998Differential equations driven by rough signals1,077 cited
  • 1998Integration with respect to fractal functions and stochastic calculus. I589 cited
  • 2002Stochastic analysis, rough path analysis and fractional Brownian motions317 cited
  • 2003Realized power variation and stochastic volatility models243 cited

Cited by

  • 2006UNIQUENESS FOR THE SIGNATURE OF A PATH OF BOUNDED VARIATION AND THE REDUCED PATH GROUP135 cited
  • 2014Smoothness of the density for solutions to Gaussian rough differential equations106 cited
  • 2016The signature of a rough path: Uniqueness94 cited
  • 2010A (rough) pathwise approach to a class of non-linear stochastic partial differential equations90 cited
  • 2013Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths88 cited
  • 2018A stochastic sewing lemma and applications84 cited
  • 2008Rough path analysis via fractional calculus80 cited
  • 2015Rough paths and 1d SDE with a time dependent distributional drift: application to polymers75 cited
  • 2014Rough paths, Signatures and the modelling of functions on streams73 cited
  • 2018Differential equations driven by rough paths with jumps64 cited
  • 2011

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Rough Burgers-like equations with multiplicative noise
59 cited
  • 2015Flows driven by rough paths57 cited
  • 2009Partial differential equations driven by rough paths56 cited
  • 2016The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory54 cited
  • 2020Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU52 cited
  • 2010Controlled differential equations as Young integrals: A simple approach51 cited