Abstract
We consider the convergence of the approximation schemes related to Itô’s integral and quadratic variation, which have been developed in Russo and Vallois (Elements of stochastic calculus via regularisation, vol. 1899, pp. 147–185, Springer, Berlin, 2007). First, we prove that the convergence in the a.s. sense exists when the integrand is Hölder continuous and the integrator is a continuous semimartingale. Second, we investigate the second order convergence in the Brownian motion case.
- Stochastic integration by regularization
- Quadratic variation
- First and second order convergence
- Stochastic Fubini’s theorem
2000 MSC: 60F05, 60F17, 60G44, 60H05, 60J65
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Bergery, B.B., Vallois, P. (2011). Convergence at First and Second Order of Some Approximations of Stochastic Integrals. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_10
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DOI: https://doi.org/10.1007/978-3-642-15217-7_10
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