Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
DOI10.1214/12-AAP890zbMath1283.60098arXiv1105.0226OpenAlexW2137519698MaRDI QIDQ373839
Peter E. Kloeden, Arnulf Jentzen, Martin Hutzenthaler
Publication date: 25 October 2013
Published in: The Annals of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1105.0226
polynomial growthstochastic differential equationsmulti-level Monte Carlonon-globally Lipschitz continuous
Monte Carlo methods (65C05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)
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- Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
- Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction
- Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model
- Convergence of the stochastic Euler scheme for locally Lipschitz coefficients
- Infinite-dimensional quadrature and approximation of distributions
- Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff
- A note on Euler's approximations
- Monte Carlo complexity of global solution of integral equations
- Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
- The Euler scheme with irregular coefficients
- The optimal uniform approximation of systems of stochastic differential equations
- Step size control for the uniform approximation of systems of stochastic differential equations with additive noise.
- Efficient Monte Carlo simulation of security prices
- Existence of strong solutions for Itô's stochastic equations via approximations
- Monte Carlo complexity of parametric integration
- Probability theory. A comprehensive course.
- Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing
- Approximation and optimization on the Wiener space
- The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations
- Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
- Multilevel Monte Carlo Path Simulation
- Comparing Hitting Time Behavior of Markov Jump Processes and Their Diffusion Approximations
- Euler Polygonal Lines for Itô Equations with Monotone Coefficients
- A Simple Proof of the Existence of a Solution of Itô’s Equation with Monotone Coefficients
- Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
- Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
- An Introduction to Financial Option Valuation
- Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients
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