Abstract

In order to calculate the Wiener integrals for functionals on Wiener space, one can usually apply the change of variable theorem. But, there are many functionals that are difficult or impossible to calculate even when using the change of variable formula. In order to solve this problem, we establish an evaluation formula via the Fourier-type functionals on Wiener space. We then present various examples to which our evaluation formula can be applied and with the corresponding numerical approximations.

中文翻译：

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基于傅立叶型泛函的维纳积分的评价公式和逼近

摘要

为了计算维纳空间上泛函的维纳积分，通常可以应用变数定理的变化。但是，即使使用变量公式的变化，也有许多难以或无法计算的泛函。为了解决这个问题，我们通过维纳空间上的傅里叶型泛函建立了一个评价公式。然后，我们展示了可以应用我们的评估公式的各种示例以及相应的数值近似值。