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

Vigirdas Mackevičius

Mathematics and Computers in Simulation (MATCOM), 1997, vol. 44, issue 2, 109-121

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.

Keywords: Stochastic differential equations; Euler scheme; Convergence rate (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:44:y:1997:i:2:p:109-121

DOI: 10.1016/S0378-4754(97)00047-5

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