Nevanlinna Theory via Stochastic Calculus

研究成果: Article

7 引用 (Scopus)

抄録

We study Nevanlinna theory using stochastic calculus. We have a defect relation for holomorphic maps in equidimensional cases which includes Carlson and Griffiths′ defect relation. The main probabilistic methods used here are some estimates on some increasing processes for Brownian motion and martingales on manifolds. The latter is obtained from Krylov′s estimate on stochastic integrals for martingales.

元の言語English
ページ(範囲)473-510
ページ数38
ジャーナルJournal of Functional Analysis
132
発行部数2
DOI
出版物ステータスPublished - 1995 9
外部発表Yes

Fingerprint

Nevanlinna Theory
Stochastic Calculus
Martingale
Defects
Holomorphic Maps
Probabilistic Methods
Stochastic Integral
Estimate
Brownian motion

ASJC Scopus subject areas

  • Analysis

これを引用

Nevanlinna Theory via Stochastic Calculus. / Atsuji, Atsushi.

:: Journal of Functional Analysis, 巻 132, 番号 2, 09.1995, p. 473-510.

研究成果: Article

@article{d58b1e7449354fa89f4eeb0ad28378a2,
title = "Nevanlinna Theory via Stochastic Calculus",
abstract = "We study Nevanlinna theory using stochastic calculus. We have a defect relation for holomorphic maps in equidimensional cases which includes Carlson and Griffiths′ defect relation. The main probabilistic methods used here are some estimates on some increasing processes for Brownian motion and martingales on manifolds. The latter is obtained from Krylov′s estimate on stochastic integrals for martingales.",
author = "Atsushi Atsuji",
year = "1995",
month = "9",
doi = "10.1006/jfan.1995.1112",
language = "English",
volume = "132",
pages = "473--510",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Nevanlinna Theory via Stochastic Calculus

AU - Atsuji, Atsushi

PY - 1995/9

Y1 - 1995/9

N2 - We study Nevanlinna theory using stochastic calculus. We have a defect relation for holomorphic maps in equidimensional cases which includes Carlson and Griffiths′ defect relation. The main probabilistic methods used here are some estimates on some increasing processes for Brownian motion and martingales on manifolds. The latter is obtained from Krylov′s estimate on stochastic integrals for martingales.

AB - We study Nevanlinna theory using stochastic calculus. We have a defect relation for holomorphic maps in equidimensional cases which includes Carlson and Griffiths′ defect relation. The main probabilistic methods used here are some estimates on some increasing processes for Brownian motion and martingales on manifolds. The latter is obtained from Krylov′s estimate on stochastic integrals for martingales.

UR - http://www.scopus.com/inward/record.url?scp=0002150755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002150755&partnerID=8YFLogxK

U2 - 10.1006/jfan.1995.1112

DO - 10.1006/jfan.1995.1112

M3 - Article

AN - SCOPUS:0002150755

VL - 132

SP - 473

EP - 510

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -