| Project/Area Number |
25610018
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 準定常分布 / 対称マルコフ過程 / 半群の超縮小性 / ヤグロム極限 / 半群のコンパクト性 / マルコフ過程の緊密性 / ディリクレ形式 |
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| Outline of Final Research Achievements |
I consider the existence and uniqueness of quasi-stationary distributions (QSD) for irreducible, strong Feller, symmetric Markov processes with tightness property. A Markov process with these properties is said to be in Class(T). I show that the semi-group of a Markov process in Class (T) is a compact operator, and thus the ground state of the Markov generator exists. We see that if the ground state is integrable with respect to the symmetrized measure, a QSD can be constructed explicitly. I can see from a result of Y. Miura, my teaching doctoral student, that if the semigroup of the symmetric Markov process in Class (T) is intrinsic ultracontractive, the existence and uniqueness of QSD follows. Combining Miura's result with Tomisaki's result on the intrinsic ultracontractivity, we can show the existence and uniqueness of QSD for one-dimensional diffusion processes in terms of speed measure and scale function.
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