@article {PagesPhamNonLinearFiltering,
	title = {Optimal quantization methods for nonlinear filtering with discrete-time observations},
	journal = {Bernoulli},
	volume = {11(5)},
	year = {2005},
	abstract = {We develop an optimal quantization approach for numerically solving nonlinear filtering problems associated with discrete-time or continuous-time state process and discrete-time observations. Two quantization methods are proposed: a marginal quantization and a Markovian quantization of the signal process. The approximate filters are explicitly solved by a finite-dimensional forward procedure. A posteriori error bounds are stated and we show that the approximate error terms are minimal at some specific grids that may be computed off-line by a stochastic gradient method based on Monte Carlo simulations. Some numerical experiments are carried out: the convergence of the approximate filter as the accuracy of the quantization increases and its stability when the latent process is mixing are emphasized.},
	keywords = {Euler scheme, Markov chain, nonlinear filtering, numerical approximation, stationary signal, stochastic gradient descent, vector quantization},
	author = {Gilles Pag{\`e}s and Huy{\^e}n Pham}
}
