Functional quantization of 1-dimensional Brownian diffusion processes

  title={Functional quantization of 1-dimensional Brownian diffusion processes},
  author={Harald Luschgy and Gilles Pag{\`e}s},
The functional quantization problem for one-dimensional Brownian diffusions on [0, T ] is investigated. First, the existence of optimal n-quantizers for every n ≥ 1 is established, based on an existence result for random vectors taking their values in abstract Banach spaces. Then, one shows under rather general assumptions that the rate of convergence of the L-quantization error is O((log n)− 1 2 ) like for the Brownian motion. Several methods to construct some quasi-optimal quantizers are… CONTINUE READING

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