Abstract
We quantize a multidimensional SDE (in the Stratonovich sense) by solving the related system of ODE’s in which the d-dimensional Brownian motion has been replaced by the components of functional stationary quantizers. We make a connection with rough path theory to show that the solutions of the quantized solutions of the ODE converge toward the solution of the SDE. On our way to this result we provide convergence rates of optimal quantizations toward the Brownian motion for \(\frac{1} {q}\)-Hölder distance, q > 2, in L p(ℙ).
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…cknowledgements
We thank A. Lejay for helpful discussions and comments about several versions of this work and F. Delarue and S. Menozzi for initiating our first “meeting” with rough path theory.
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Pagès, G., Sellami, A. (2011). Convergence of Multi-Dimensional Quantized SDE’s. 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_11
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DOI: https://doi.org/10.1007/978-3-642-15217-7_11
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