Distributional It\^o's Formula and Regularization of Generalized Wiener Functionals

Takafumi Amaba; Yoshihiro Ryu

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arXiv · 1607.03596

Distributional It\^o's Formula and Regularization of Generalized Wiener Functionals

Takafumi Amaba·Yoshihiro Ryu

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Abstract

We investigate Bochner integrabilities of generalized Wiener functionals. We further formulate an It\^o formula for a diffusion in a distributional setting, and apply to investigate differentiability-index $s$ and integrability-index $p \geqslant 2$ for which the Bochner integral belongs to $\mathbb{D}_{p}^{s}$.

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Takafumi Amaba, Yoshihiro Ryu. 2016-07-13. Distributional It\^o's Formula and Regularization of Generalized Wiener Functionals. https://arxiv.org/abs/1607.03596

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