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

Gilles Pagès (1) , Abass Sagna (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

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

Domains: Probability [math.PR]

Gilles Pagès, Abass Sagna. Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering. 2015. ⟨hal-01211285v2⟩