Convergence of multi-dimensional quantized $SDE$'s

Abstract

We quantize a multidimensional $SDE$ (in the Stratonovich sense) by solving the related system of $ODE$'s in which the $d$-dimensional Brownian motion has been replaced by the components of functional stationary quantizers. We make a connection with rough path theory to show that the solutions of the quantized solutions of the $ODE$ converge toward the solution of the $SDE$. On our way to this result we provide convergence rates of optimal quantizations toward the Brownian motion for $\frac{1}{q}$-H\" older distance, $q>2$, in $L^p(\P )$.

43 pages

References in corpus (5)

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Cited by in corpus (5)

• Quadratic optimal functional quantization of stochastic processes and numerical applications
• Pathwise approximation of SDEs by coupling piecewise abelian rough paths
• Rough functional quantization and the support of McKean-Vlasov equations
• A Dynamical Sparse Grid Collocation Method for Differential Equations Driven by White Noise
• Reduced basis techniques for stochastic problems