# Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering

Abstract : 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
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01211285
Contributor : Abass Sagna <>
Submitted on : Wednesday, July 19, 2017 - 11:13:20 PM
Last modification on : Friday, March 27, 2020 - 3:54:32 AM

### Files

SPA_3147_Long.pdf
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### Identifiers

• HAL Id : hal-01211285, version 3
• ARXIV : 1510.01048

### Citation

Gilles Pagès, Abass Sagna. Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering. 2015. ⟨hal-01211285v3⟩

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