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Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation
6 references·16 citing·33 second hop
Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation (2008)Differential Equations Driven by Rough Pa…Numerical solution of stochastic differential equations (2016)Numerical solution of stochas…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…Stochastic calculus with anticipating integrands (1988)Stochastic calculus with anti…Stochastic Differential Equations and Diffusion Processes (1983)Stochastic Differential Equat…First-order Euler scheme for SDEs driven by fractional Brownian motions: The rough case (2019)First-order Euler scheme for …A priori estimates for rough PDEs with application to rough conservation laws (2019)A priori estimates for rough …Differential equations driven by rough paths with jumps (2018)Differential equations driven…Pathwise stochastic integrals for model free finance (2016)Pathwise stochastic integrals…Geometric versus non-geometric rough paths (2015)Geometric versus non-geometri…Flows driven by rough paths (2015)Flows driven by rough pathsEvolving communities with individual preferences (2014)Evolving communities with ind…Wong–Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces (2013)Wong–Zakai approximation of s…Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions (2013)Upper bounds for the density …Integrability and tail estimates for Gaussian rough differential equations (2013)Integrability and tail estima…0 A MILSTEIN-TYPE SCHEME WITHOUT LEVY AREA TERMS FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION (2013)0 A MILSTEIN-TYPE SCHEME WITH…Continuous-time trading and the emergence of probability (2012)Continuous-time trading and t…A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion (2012)A Milstein-type scheme withou…Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/2 (2011)Existence and Uniqueness of t…A generalized Fernique theorem and applications (2010)A generalized Fernique theore…Euler estimates for rough differential equations (2007)Euler estimates for rough dif…Multiple Wiener Integral (1951)Stochastic calculus of variations and hypoelliptic operators (1978)A generalized clark representation formula, with application to optimal portfolios (1991)Forward, backward and symmetric stochastic integration (1993)Backward doubly stochastic differential equations and systems of quasilinear SPDEs (1994)Controlling rough paths (2004)Multidimensional Stochastic Processes as Rough Paths (2010)A regularity structure for rough volatility (2019)Hörmander’s theorem for semilinear SPDEs (2019)The Malliavin Calculus and Related Topics (1995)Characteristic functions of measures on geometric rough paths (2016)From Rough Path Estimates to Multilevel Monte Carlo (2016)The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory (2016)Continuous Martingales and Brownian Motion (1999)Limit Theorems for Stochastic Processes (2003)Brownian Motion and Stochastic Calculus (2007)Pathwise stochastic calculus with local times (2018)Robust pricing–hedging dualities in continuous time (2018)Stochastic Integration and Differential Equations (2005)Canonical RDEs and general semimartingales as rough paths (2018)Analysis of the Rosenblatt process (2008)Stochastic heat equation driven by fractional noise and local time (2008)Averaging along irregular curves and regularisation of ODEs (2016)Martingale Methods in Financial Modelling (1997)Alternative models for stock price dynamics (2003)Multilevel Monte Carlo Path Simulation (2008)Differential equations driven by fractional Brownian motion (2002)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)An Overview of Value at Risk (1997)Pricing the risks of default (1998)Robustness of the Black and Scholes Formula (1998)
this work references cited by second hop

References

  • 2016Numerical solution of stochastic differential equations5,001 cited
  • 1983Stochastic Differential Equations and Diffusion Processes3,836 cited
  • 1998Stochastic Flows and Stochastic Differential Equations1,182 cited
  • 1998Differential equations driven by rough signals1,077 cited
  • 2002System Control and Rough Paths519 cited
  • 1988Stochastic calculus with anticipating integrands496 cited

Cited by

  • 2015Geometric versus non-geometric rough paths85 cited
  • 2013Integrability and tail estimates for Gaussian rough differential equations85 cited
  • 2018Differential equations driven by rough paths with jumps64 cited
  • 2012Continuous-time trading and the emergence of probability64 cited
  • 2011Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/260 cited
  • 2015Flows driven by rough paths57 cited
  • 2012A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion55 cited
  • 2019A priori estimates for rough PDEs with application to rough conservation laws53 cited
  • 2016Pathwise stochastic integrals for model free finance

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51 cited
  • 2007Euler estimates for rough differential equations51 cited
  • 20130 A MILSTEIN-TYPE SCHEME WITHOUT LEVY AREA TERMS FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION48 cited
  • 2010A generalized Fernique theorem and applications41 cited
  • 2019First-order Euler scheme for SDEs driven by fractional Brownian motions: The rough case38 cited
  • 2013Wong–Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces38 cited
  • 2013Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions35 cited
  • 2014Evolving communities with individual preferences33 cited