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A Local Refinement Strategy for Constructive Quantization of Scalar SDEs

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Abstract

We present a fully constructive method for quantization of the solution X of a scalar SDE in the path space L p [0,1] or C[0,1]. The construction relies on a refinement strategy which takes into account the local regularity of X and uses Brownian motion (bridge) quantization as a building block. Our algorithm is easy to implement, its computational cost is close to the size of the quantization, and it achieves strong asymptotic optimality provided this property holds for the Brownian motion (bridge) quantization.

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Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Priority Programme 1324. We are grateful to Stephan Toussaint for the implementation of our quantization method, and we thank Robert Offinger for his technical support.

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Authors and Affiliations

  1. Fakultät für Informatik und Mathematik, Universität Passau, Innstr. 33, 94030, Passau, Germany

    Thomas Müller-Gronbach

  2. Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany

    Klaus Ritter

Authors
  1. Thomas Müller-Gronbach
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  2. Klaus Ritter
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Correspondence to Thomas Müller-Gronbach.

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Communicated by Peter Kloeden.

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Müller-Gronbach, T., Ritter, K. A Local Refinement Strategy for Constructive Quantization of Scalar SDEs. Found Comput Math 13, 1005–1033 (2013). https://doi.org/10.1007/s10208-013-9160-1

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  • DOI: https://doi.org/10.1007/s10208-013-9160-1

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