Two approaches are suggested for constructing a probabilistic approximation of the evolution operator e–itH, where $$H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}$$ , in the strong operator topology. In the first approach, the approximating operators have the form of expectations of functionals of a certain Poisson point field, while, in the second approach, the approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables with finite moments of order 2m + 2.

中文翻译：

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进化算子的概率近似——itHwhere$$H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{ {2m}}}}}{{d{{x}^{{2m}}}}}$$

建议使用两种方法来构建进化算子 e-itH 的概率近似，其中 $$H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}} \tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}$$ ，在强算子拓扑中。在第一种方法中，逼近算子具有某个泊松点域的泛函期望形式，而在第二种方法中，逼近算子具有具有有限矩的独立同分布随机变量之和的泛函期望形式2m + 2 阶。