Symmetric Markov processes and Dirichlet forms
对称马尔可夫过程和狄利克雷形式
基本信息
- 批准号:09640265
- 负责人:
- 金额:$ 1.73万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:1997
- 资助国家:日本
- 起止时间:1997 至 1999
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The objective of this study is to investigate symmetric Markov processes by using Dirichlet form theory. Symmetric Markov processes are a special class in Donsker-Varadhan type large deviation theory in the sense that the rate functions of large deviation principle are given by the associated Dirichlet forms. In 1984, Fukushima and I showed that symmetric Markov processes can be transformed to ergodic processes by some supermartingale multiplicative functionals even if a symmetric Markov process is explosive or has the killing inside. As a result, Donsker-Varadhan type large deviation principle could be extended to symmetric Markov processes with finite lifetime. In this study, I found a new sufficient condition for the upper estimate holding for not only compact sets but also for closed sets. In fact, I showed that the full large deviation principle holds if the Markov process explodes so fast that the 1-resolvent of the identity function belongs to the space of continuous functions vanishing at infinity. As a corollary of this result, I showed LィイD1pィエD1-independence of the spectral radius of symmetric Markov semigroups. And I applied it to obtain a necessary and sufficient condition for the integrability of Feynman-Kac functionals. This result also gives us an criterion whether a Schrodinger operators is subcritical or not.We further extended the large deviation principle to Markov processes with Feynman-Kac functional, and consider asymptotic properties of Feynman-Kac semigroups.
本文利用Dirichlet型理论研究对称马氏过程。对称马氏过程是Donsker-Varadhan型大偏差理论中的一个特殊类,它的大偏差原理的速率函数由相应的Dirichlet形式给出. 1984年,福岛和我证明了即使对称马氏过程是爆炸的或内部有杀戮,对称马氏过程也可以通过上鞅乘法泛函转化为遍历过程。结果表明,Donsker-Varadhan型大偏差原理可以推广到有限寿命的对称马氏过程。在这项研究中,我发现了一个新的充分条件,不仅对紧集,而且对闭集的上估计成立。事实上,我证明了,如果马尔可夫过程爆炸得如此之快,以至于单位函数的1-预解式属于在无穷远处消失的连续函数空间,则完全大偏差原理成立。作为这个结果的推论,我证明了对称马氏半群的谱半径的L D1 p D1-独立性。并应用它得到了Feynman-Kac泛函可积的一个充分必要条件。我们进一步将大偏差原理推广到具有Feynman-Kac泛函的马氏过程,并研究了Feynman-Kac半群的渐近性质。
项目成果
期刊论文数量(26)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
M. Takeda: "Large deviations and LIL's for Brownian motions on Nested fractals"Osaka J. Math.. (to appear).
M. Takeda:“嵌套分形上布朗运动的大偏差和 LIL”Osaka J. Math..(即将出现)。
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竹田 雅好: "Large deviations and LIL's for Brownian motions on nested Fractals"Osaka J. Math.. in Press.
Masayoshi Takeda:“嵌套分形上布朗运动的大偏差和 LIL”Osaka J. Math.. 正在出版。
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竹田雅好: "Large deviations and LIL's for Brownian motions on nested fractals"to appear in Osaka J. Math..
Masayoshi Takeda:“嵌套分形上布朗运动的大偏差和 LIL”出现在 Osaka J. Math..
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長井 英生: "Ergodic type Bellman equations of risk-sensitive control with large parameters and singular limits"Asymptotic Analysic. 20. 279-299 (1999)
Hideo Nagai:“具有大参数和奇异极限的风险敏感控制的遍历型贝尔曼方程”渐近分析 20. 279-299 (1999)
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竹田雅好: "Asymptotic propeties of generalized Feynmam-Kac functionals" Potential Analysis. 9. 261-291 (1998)
Masayoshi Takeda:“广义 Feynmam-Kac 泛函的渐近性质”潜在分析 9. 261-291 (1998)。
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TAKEDA Masayoshi其他文献
TAKEDA Masayoshi的其他文献
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{{ truncateString('TAKEDA Masayoshi', 18)}}的其他基金
Functional analytic study on asymptotic properties of Markov processes
马尔可夫过程渐近性质的泛函分析研究
- 批准号:
22340024 - 财政年份:2010
- 资助金额:
$ 1.73万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Dirichlet Forms and Stochastic Analysis of Symmetric Markov Processes
对称马尔可夫过程的狄利克雷形式和随机分析
- 批准号:
18340033 - 财政年份:2006
- 资助金额:
$ 1.73万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Large deviations for symmetric Markov processes and Dirichlet forms
对称马尔可夫过程和狄利克雷形式的大偏差
- 批准号:
15540103 - 财政年份:2003
- 资助金额:
$ 1.73万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Symmetric Markov processes and large deviation theory
对称马尔可夫过程和大偏差理论
- 批准号:
12640099 - 财政年份:2000
- 资助金额:
$ 1.73万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
相似海外基金
Overviews and constructions of Dirichlet form theory on non-Archimedean space on a basis of hierarchical structure
基于层次结构的非阿基米德空间狄利克雷形式理论概述与构建
- 批准号:
26400150 - 财政年份:2014
- 资助金额:
$ 1.73万 - 项目类别:
Grant-in-Aid for Scientific Research (C)