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First order strong approximations of scalar SDEs defined in a domain
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References

  • 2007Brownian Motion and Stochastic Calculus7,421 cited
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  • 2008Multilevel Monte Carlo Path Simulation1,436 cited
  • 2012Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients428 cited
  • 2009A comparison of biased simulation schemes for stochastic volatility models316 cited
  • 2008Simple and efficient simulation of the Heston stochastic volatility model266 cited
  • 2005On the discretization schemes for the CIR (and Bessel squared) processes246 cited
  • 2007Improved Multilevel Monte Carlo Convergence using the Milstein Scheme205 cited
  • 2005Convergence of Monte Carlo simulations involving the mean-reverting square root process162 cited
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Cited by

  • 2020On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients

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128 cited
  • 2015Loss of regularity for Kolmogorov equations81 cited
  • 2016An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients64 cited
  • 2020Mean-square convergence rates of stochastic theta methods for SDEs under a coupled monotonicity condition58 cited
  • 2024Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations52 cited
  • 2017Strong convergence rates for Cox–Ingersoll–Ross processes — Full parameter range41 cited
  • 2019Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion37 cited
  • 2015Multilevel Monte Carlo Quadrature of Discontinuous Payoffs in the Generalized Heston Model Using Malliavin Integration by Parts33 cited
  • 2016A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models33 cited
  • 2016On stochastic differential equations with arbitrary slow convergence rates for strong approximation30 cited
  • 2018On arbitrarily slow convergence rates for strong numerical approximations of Cox–Ingersoll–Ross processes and squared Bessel processes27 cited
  • 2023Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients24 cited
  • 2019The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate22 cited
  • 2014Construction of positivity preserving numerical schemes for some multidimensional stochastic differential equations18 cited