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Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations
2 references·9 citing·37 second hop
Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations (2000)Convergence of numerical schemes for the …Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II (1999)Lattice Approximations for St…Stochastic Differential Equations and Diffusion Processes (1983)Stochastic Differential Equat…On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients (2020)On a perturbation theory and …Stochastic Gradient Descent in Continuous Time (2017)Stochastic Gradient Descent i…TAYLOR EXPANSIONS OF SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE1 (2016)TAYLOR EXPANSIONS OF SOLUTION…2 APPROXIMATING ROUGH STOCHASTIC PDES (2016)2 APPROXIMATING ROUGH STOCHAS…Loss of regularity for Kolmogorov equations (2015)Loss of regularity for Kolmog…Weak approximation of stochastic partial differential equations: the nonlinear case (2010)Weak approximation of stochas…Taylor expansions of solutions of stochastic partial differential equations with additive noise (2010)Taylor expansions of solution…Optimal Pointwise Approximation of a Linear Stochastic Heat Equation with Additive Space-Time White Noise (2007)Optimal Pointwise Approximati…An implicit Euler scheme with non-uniform time discretization for heat equations with multiplicative noise (2007)An implicit Euler scheme with…Controlled Diffusion Processes (1980)Existence of strong solutions for Itô's stochastic equations via approximations (1996)An introduction to stochastic partial differential equations (2006)Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients (2014)A mild Itô formula for SPDEs (2018)The Malliavin Calculus and Related Topics (1995)The Malliavin Calculus and Related Topics (2006)Duality in refined Sobolev–Malliavin spaces and weak approximation of SPDE (2015)Numerical solution of stochastic differential equations (2016)Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient (2018)Stochastic evolution equations in (1999)The Optimal Discretization of Stochastic Differential Equations (2001)Stochastic Differential Equations: An Introduction with Applications. (1987)Stochastic Differential Equations (2006)Convergence of the Euler–Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient (2017)Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks (2020)Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations (2024)A Note on Euler's Approximations (1998)A Concise Course on Stochastic Partial Differential Equations (2007)Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients (2008)Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises (2012)Multilevel Monte Carlo Path Simulation (2008)Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients (2010)On stochastic differential equations with arbitrary slow convergence rates for strong approximation (2016)Multilevel Picard iterations for solving smooth semilinear parabolic heat equations (2021)An equilibrium characterization of the term structure (1977)Specification Analysis of Affine Term Structure Models (2000)Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach (2002)Universal Features of Price Formation in Financial Markets: Perspectives From Deep Learning (2018)Deep Learning Volatility (2019)Online parameter estimation for the McKean–Vlasov stochastic differential equation (2023)Brownian Motion and Stochastic Calculus (1998)Differential equations driven by rough signals (1998)Brownian Motion and Stochastic Calculus (2007)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)
this work references cited by second hop

References

  • 1983Stochastic Differential Equations and Diffusion Processes3,836 cited
  • 1999Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II227 cited

Cited by

  • 2010Weak approximation of stochastic partial differential equations: the nonlinear case129 cited
  • 2020On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients128 cited
  • 2015Loss of regularity for Kolmogorov equations81 cited
  • 2017Stochastic Gradient Descent in Continuous Time55 cited
  • 2016TAYLOR EXPANSIONS OF SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE153 cited
  • 2010Taylor expansions of solutions of stochastic partial differential equations with additive noise49 cited
  • 2007An implicit Euler scheme with non-uniform time discretization for heat equations with multiplicative noise38 cited
  • 20162 APPROXIMATING ROUGH STOCHASTIC PDES32 cited
  • 2007Optimal Pointwise Approximation of a Linear Stochastic Heat Equation with Additive Space-Time White Noise27 cited

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