Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering
Résumé
We take advantage of recent (see~\cite{GraLusPag1, PagWil}) and new results on optimal quantization theory to improve the quadratic optimal quantization error bounds for backward stochastic differential equations (BSDE) and nonlinear filtering problems. For both problems, a first improvement relies on a Pythagoras like Theorem for quantized conditional expectation. While allowing for some locally Lipschitz functions conditional densities in nonlinear filtering, the analysis of the error brings into playing a new robustness result about optimal quantizers, the so-called distortion mismatch property: $L^r$-quadratic optimal quantizers of size $N$ behave in $L^s$ in term of mean error at the same rate $N^{-\frac 1d}$, $0
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Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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https://hal.science/hal-01211285
Soumis le : mercredi 19 juillet 2017-23:13:20
Dernière modification le : jeudi 2 mai 2024-13:57:37
Citer
Gilles Pagès, Abass Sagna. Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering. Stochastic Processes and their Applications, 2018, 128, pp.847-883. ⟨hal-01211285v3⟩
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