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PRACTICAL VARIANCE REDUCTION VIA REGRESSION FOR SIMULATING DIFFUSIONS

机译:通过回归模拟扩散降低实际方差

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摘要

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.
机译:如果已知所需解的近似值,则可以利用众所周知的方差减少方法(重要性抽样方法和控制变量方法)。在这里,我们使用条件概率表示的解以及回归方法,通过使用从初始位置开始的一组近似轨迹来获得足够便宜(尽管相当粗略)的解及其派生估计。这些估计可以有效地用于显着减少方差并进一步精确评估所需的解决方案。数值实验支持了所开发的方法。

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