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Probability density estimation in stochastic environmental models using reverse representations

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Abstract

The estimation of probability densities of variables described by stochastic differential equations has long been done using forward time estimators, which rely on the generation of forward in time realizations of the model. Recently, an estimator based on the combination of forward and reverse time estimators has been developed. This estimator has a higher order of convergence than the classical one. In this article, we explore the new estimator and compare the forward and forward–reverse estimators by applying them to a biochemical oxygen demand model. Finally, we show that the computational efficiency of the forward–reverse estimator is superior to the classical one, and discuss the algorithmic aspects of the estimator.

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Acknowledgements

The authors would like to thank G.N. Milstein for helpful discussions and comments.

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Authors and Affiliations

  1. Department of Applied Mathematical Analysis, Delft University of Technology Faculty of Information Technology and Systems, Mekelweg 4, 2628, CD Delft, The Netherlands

    E. van den. Berg, A. W. Heemink & H. X. Lin

  2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany

    J. G. M. Schoenmakers

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  1. E. van den. Berg
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  2. A. W. Heemink
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  3. H. X. Lin
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  4. J. G. M. Schoenmakers
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Correspondence to A. W. Heemink.

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Berg, E.v.d., Heemink, A.W., Lin, H.X. et al. Probability density estimation in stochastic environmental models using reverse representations. Stoch Environ Res Ris Assess 20, 126–139 (2006). https://doi.org/10.1007/s00477-005-0022-5

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  • DOI: https://doi.org/10.1007/s00477-005-0022-5

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