An application of the partial malliavin calculus to baouendi–grushin operators

Setsuo Taniguchi

doi:10.2206/kyushujm.73.417

An application of the partial malliavin calculus to baouendi–grushin operators

Setsuo Taniguchi

Division for Theoretical Natural Science

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The existence and the continuity of the transition density function of the diffusion process generated by the Baouendi–Grushin operator is shown with the help of the partial Malliavin calculus. For this purpose, the partial Malliavin calculus is reformulated in terms of Watanabe’s distribution theory on Wiener spaces.

Original language	English
Pages (from-to)	417-431
Number of pages	15
Journal	Kyushu Journal of Mathematics
Volume	73
Issue number	2
DOIs	https://doi.org/10.2206/kyushujm.73.417
Publication status	Published - 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.2206/kyushujm.73.417

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title = "An application of the partial malliavin calculus to baouendi–grushin operators",

abstract = "The existence and the continuity of the transition density function of the diffusion process generated by the Baouendi–Grushin operator is shown with the help of the partial Malliavin calculus. For this purpose, the partial Malliavin calculus is reformulated in terms of Watanabe{\textquoteright}s distribution theory on Wiener spaces.",

author = "Setsuo Taniguchi",

note = "Funding Information: is also continuous for any 1 < p < ∞. Owing to these continuities, the expression (21) implies the continuity of qT in (ξ, η) ∈ Rd1 × Rd2. 2 Acknowledgement. This work was supported by JSPS KAKENHI Grant Number JP18K03336. Publisher Copyright: {\textcopyright} 2019 Faculty of Mathematics, Kyushu University.",

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language = "English",

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N1 - Funding Information: is also continuous for any 1 < p < ∞. Owing to these continuities, the expression (21) implies the continuity of qT in (ξ, η) ∈ Rd1 × Rd2. 2 Acknowledgement. This work was supported by JSPS KAKENHI Grant Number JP18K03336. Publisher Copyright: © 2019 Faculty of Mathematics, Kyushu University.

PY - 2019

Y1 - 2019

N2 - The existence and the continuity of the transition density function of the diffusion process generated by the Baouendi–Grushin operator is shown with the help of the partial Malliavin calculus. For this purpose, the partial Malliavin calculus is reformulated in terms of Watanabe’s distribution theory on Wiener spaces.

AB - The existence and the continuity of the transition density function of the diffusion process generated by the Baouendi–Grushin operator is shown with the help of the partial Malliavin calculus. For this purpose, the partial Malliavin calculus is reformulated in terms of Watanabe’s distribution theory on Wiener spaces.

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An application of the partial malliavin calculus to baouendi–grushin operators

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