Probability density estimation in stochastic environmental models using reverse representations |
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Authors: | E. van den. Berg A. W. Heemink H. X. Lin J. G. M. Schoenmakers |
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Affiliation: | (1) Department of Applied Mathematical Analysis, Delft University of Technology Faculty of Information Technology and Systems, Mekelweg 4, 2628 CD Delft, The Netherlands;(2) Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany |
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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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