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Functional quantization of a class of Brownian diffusions: A constructive approach

Author

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  • Luschgy, Harald
  • Pagès, Gilles

Abstract

The functional quantization problem for one-dimensional Brownian diffusions on [0,T] is investigated. One shows under rather general assumptions that the rate of convergence of the Lp-quantization error is like for the Brownian motion. Several methods to construct some rate-optimal quantizers are proposed. These results are extended to d-dimensional diffusions when the diffusion coefficient is the inverse of a gradient function. Finally, a special attention is given to diffusions with a Gaussian martingale term.

Suggested Citation

  • Luschgy, Harald & Pagès, Gilles, 2006. "Functional quantization of a class of Brownian diffusions: A constructive approach," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 310-336, February.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:2:p:310-336
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    Citations

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    Cited by:

    1. Frikha Noufel & Sagna Abass, 2012. "Quantization based recursive importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 287-326, December.
    2. Antoine Jacquier & Louis Jeannerod, 2017. "How many paths to simulate correlated Brownian motions?," Papers 1708.05352, arXiv.org.
    3. Ren'e Aid & Lamia Ben Ajmia & M'hamed Gaigi & Mohamed Mnif, 2021. "Nonzero-sum stochastic impulse games with an application in competitive retail energy markets," Papers 2112.10213, arXiv.org.
    4. Ofelia Bonesini & Giorgia Callegaro & Martino Grasselli & Gilles Pag`es, 2023. "From elephant to goldfish (and back): memory in stochastic Volterra processes," Papers 2306.02708, arXiv.org, revised Sep 2023.
    5. Sagna, Abass, 2011. "Pricing of barrier options by marginal functional quantization," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 371-398, December.
    6. Miranda, Manuel J. & Bocchini, Paolo, 2015. "A versatile technique for the optimal approximation of random processes by Functional Quantization," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 935-958.
    7. Møller, Jan Kloppenborg & Madsen, Henrik & Carstensen, Jacob, 2011. "Parameter estimation in a simple stochastic differential equation for phytoplankton modelling," Ecological Modelling, Elsevier, vol. 222(11), pages 1793-1799.
    8. Bonollo, Michele & Di Persio, Luca & Oliva, Immacolata, 2020. "A quantization approach to the counterparty credit exposure estimation," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 335-356.
    9. Dereich, Steffen, 2008. "The coding complexity of diffusion processes under Lp[0,1]-norm distortion," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 938-951, June.
    10. Dereich, Steffen, 2008. "The coding complexity of diffusion processes under supremum norm distortion," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 917-937, June.
    11. Corlay Sylvain & Pagès Gilles, 2015. "Functional quantization-based stratified sampling methods," Monte Carlo Methods and Applications, De Gruyter, vol. 21(1), pages 1-32, March.

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