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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1002/ncr.4110060210

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0945-3245

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Pathwise approximation of stochastic differential

Authors: A Jentzen P E Kloeden A Neuenkirch
Publish Date: 2008/11/27
Volume: 112, Issue: 1, Pages: 41-64
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Abstract

We study the approximation of stochastic differential equations on domains For this we introduce modified Itô–Taylor schemes which preserve approximately the boundary domain of the equation under consideration Assuming the existence of a unique nonexploding solution we show that the modified Itô–Taylor scheme of order γ has pathwise convergence order γ − ε for arbitrary ε  0 as long as the coefficients of the equation are sufficiently differentiable In particular no global Lipschitz conditions for the coefficients and their derivatives are required This applies for example to the so called square root diffusions

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  2. A new class of symplectic integration schemes based on generating functions
  3. An optimal adaptive finite element method for elastoplasticity
  4. Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
  5. Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain
  6. Decay rates of adaptive finite elements with Dörfler marking
  7. Multi-parameter regularization and its numerical realization
  8. Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes
  9. Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation
  10. A uniformly stable Fortin operator for the Taylor–Hood element
  11. A locking-free $$hp$$ DPG method for linear elasticity with symmetric stresses
  12. The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem
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  14. Multi-level spectral galerkin method for the navier-stokes problem I : spatial discretization
  15. Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods
  16. A residual–based error estimator for BEM–discretizations of contact problems
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  19. Symmetric multistep methods for constrained Hamiltonian systems
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  22. Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces
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  26. On generalized successive overrelaxation methods for augmented linear systems
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