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# Title: Convergence of multi-dimensional quantized $SDE$'s

Authors: Gilles Pagès (PMA), Afef Sellami (PMA)
Abstract: We quantize a multidimensional $SDE$ (in the Stratanovich sense) by solving the related $ODE$'s in which the Brownian motion has been replaced by the components of stationary quantizers. We make a connection with rough path theory to show that such quantizations converge toward the solution of the $SDE$. In some particular cases, we show that this procedure provide some rate optimal quantizations of the equation.
 Comments: 22 pages Subjects: Probability (math.PR) Cite as: arXiv:0801.0726 [math.PR] (or arXiv:0801.0726v1 [math.PR] for this version)

## Submission history

From: Gilles Pages [view email]
[v1] Fri, 4 Jan 2008 19:47:33 GMT (22kb)
[v2] Tue, 6 Jul 2010 08:06:26 GMT (32kb)
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