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A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations
16 references·1 citing·35 second hop
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References

  • 2010Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients431 cited
  • 2012Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients428 cited
  • 1996Existence of strong solutions for Itô's stochastic equations via approximations400 cited
  • 2014Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients227 cited
  • 2016THE 4/2 STOCHASTIC VOLATILITY MODEL: A UNIFIED APPROACH FOR THE HESTON AND THE 3/2 MODEL163 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
  • 2013Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations78 cited
  • 2016An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients64 cited
  • 2010Stochastic flows and Bismut formulas for stochastic Hamiltonian systems62 cited
  • 1990Stochastic Integrals57 cited
  • 2024Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations52 cited
  • 2013A STOCHASTIC GRONWALL LEMMA52 cited

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2007
Global flows for stochastic differential equations without global Lipschitz conditions
38 cited
  • 2011Lack of strong completeness for stochastic flows24 cited
  • 2018A class of stochastic Gronwall’s inequality and its application22 cited
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    • 2020Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities17 cited