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|Title:||Practical Variance Reduction via Regression for Simulating Diffusions|
|Authors:||Milstein, G. N.|
Tretyakov, Michael V.
|Publisher:||Society for Industrial and Applied Mathematics|
|Citation:||SIAM Journal on Numerical Analysis, 2009, 47 (2), pp. 887-910.|
|Abstract:||The well-known variance reduction methods—the method of importance sampling and the method of control variates—can be exploited if an approximation of the required solution is known. Here we employ conditional probabilistic representations of solutions together with the regression method to obtain sufficiently inexpensive (although rather rough) estimates of the solution and its derivatives by using the single auxiliary set of approximate trajectories starting from the initial position. These estimates can effectively be used for significant reduction of variance and further accurate evaluation of the required solution. The developed approach is supported by numerical experiments.|
|Rights:||This paper was published as SIAM Journal on Numerical Analysis, 2009, 47 (2), pp. 887-910. Copyright © 2009 Society for Industrial and Applied Mathematics. It is available from http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM. Doi: 10.1137/060674661|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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