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Convergence rate of Euler scheme for stochastic differential equations: Functionals of solutions

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  • Mackevičius, Vigirdas

Abstract

Let Xt, t ∈ [0,T], be the solution of a stochastic differential equation, and let Xth, t ∈ [0,T], be the Euler approximation with the step h = Tn. It is known that, for a wide class of functions f, the error Ef(XTh) − Ef(XT) is O(h) or, more exactly, C · h + O(h2). We propose an extension of these results to a class of functionals f depending on the trajectories of the solution on the whole time interval [0,T]. The functionals are defined on an appropriate semi-martingale space.

Suggested Citation

  • Mackevičius, Vigirdas, 1997. "Convergence rate of Euler scheme for stochastic differential equations: Functionals of solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(2), pages 109-121.
    • Handle: RePEc:eee:matcom:v:44:y:1997:i:2:p:109-121
    DOI: 10.1016/S0378-4754(97)00047-5
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    References listed on IDEAS

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    1. Remigijus Mikulevicius & Eckhard Platen, 1991. "Rate of Convergence of the Euler Approximation for Diffusion Processes," Published Paper Series 1991-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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