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
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Probability [math.PR]
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https://hal.science/hal-01211285
Submitted on : Wednesday, July 19, 2017-11:13:20 PM
Last modification on : Thursday, March 14, 2024-3:11:55 AM
Cite
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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