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From Rough Path Estimates to Multilevel Monte Carlo
12 references·2 citing·38 second hop
From Rough Path Estimates to Multilevel Monte Carlo (2016)From Rough Path Estimates to Multilevel M…The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory (2016)The Jain–Monrad criterion for…Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation (2014)Antithetic multilevel Monte C…A continuation multilevel Monte Carlo algorithm (2014)A continuation multilevel Mon…Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths (2013)Regularity of laws and ergodi…Integrability and tail estimates for Gaussian rough differential equations (2013)Integrability and tail estima…Convergence rates for the full Gaussian rough paths (2013)Convergence rates for the ful…A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion (2012)A Milstein-type scheme withou…Differential equations driven by Gaussian signals (2010)Differential equations driven…Densities for rough differential equations under Hörmander’s condition (2010)Densities for rough different…Multilevel Monte Carlo Path Simulation (2008)Multilevel Monte Carlo Path S…Stochastic analysis, rough path analysis and fractional Brownian motions (2002)Stochastic analysis, rough pa…Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution (1986)Discrétisation d'une équation…First-order Euler scheme for SDEs driven by fractional Brownian motions: The rough case (2019)First-order Euler scheme for …Rough differential equations with unbounded drift term (2016)Rough differential equations …Stochastic Differential Equations and Diffusion Processes (1983)Continuous Martingales and Brownian Motion (1999)Stochastic integration with respect to fractional brownian motion (2003)Brownian Motion and Stochastic Calculus (2007)Differential Equations Driven by Rough Paths (2007)Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008)Differential equations driven by rough signals (1998)System Control and Rough Paths (2002)Multidimensional Stochastic Processes as Rough Paths (2010)Approximation of SDEs: a stochastic sewing approach (2021)Fractional Brownian Motions, Fractional Noises and Applications (1968)The Malliavin Calculus and Related Topics (2006)Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion (2008)Smoothness of the density for solutions to Gaussian rough differential equations (2014)Stochastic Differential Equations (1998)Monte Carlo Methods in Financial Engineering (2003)A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2015)Unbiased Estimation with Square Root Convergence for SDE Models (2015)Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain (2018)A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993)Multilevel Richardson–Romberg extrapolation (2017)Multilevel Nested Simulation for Efficient Risk Estimation (2019)Modern Bayesian Experimental Design (2024)The Malliavin Calculus and Related Topics (1995)Characteristic functions of measures on geometric rough paths (2016)On probability laws of solutions to differential systems driven by a fractional Brownian motion (2016)Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients (2012)Numerical solution of stochastic differential equations (2016)Optimal Model Management for Multifidelity Monte Carlo Estimation (2016)Discretization and simulation of stochastic differential equations (1985)Rate of Convergence of the Euler Approximation for Diffusion Processes (1991)Error estimates for the binomial approximation of American put options (1998)Numerical Approximation for Functionals of Reflecting Diffusion Processes (1998)Efficient numerical schemes for the approximation of expectations of functionals of the solution of a S.D.E., and applications (2005)Rough paths, Signatures and the modelling of functions on streams (2014)C∞− regularization of ODEs perturbed by noise (2021)A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2010)
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References

  • 2008Multilevel Monte Carlo Path Simulation1,436 cited
  • 2002Stochastic analysis, rough path analysis and fractional Brownian motions317 cited
  • 2010Densities for rough differential equations under Hörmander’s condition131 cited
  • 2014A continuation multilevel Monte Carlo algorithm121 cited
  • 2010Differential equations driven by Gaussian signals113 cited
  • 2014Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation109 cited
  • 2013Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths88 cited
  • 2013Integrability and tail estimates for Gaussian rough differential equations85 cited
  • 1986Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution76 cited
  • 2013Convergence rates for the full Gaussian rough paths56 cited
  • 2012A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion55 cited
  • 2016The Jain–Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory54 cited

Cited by

  • 2019First-order Euler scheme for SDEs driven by fractional Brownian motions: The rough case38 cited
  • 2016Rough differential equations with unbounded drift term

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37 cited