2011 Fiscal Year Final Research Report
New development of excursion theory for Markov processes
| Project/Area Number |
20740060
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University (2011)
Kobe University (2008-2010) |
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Principal Investigator |
YANO Kouji 京都大学, 大学院・理学研究科, 准教授 (80467646)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 数学一般(含確率論・統計数学) |
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| Research Abstract |
I have made new developments of excursion theory for Markov processes from the following four viewpoints.(1) The penalisation problems, i. e., the limit problems of Markov processes transformed by weight and normalization.(2) Extension of diffusion process on intervals which involves jumps from the boundaries.(3) Extremality of excursion measures and the sigma-finite measures unifying penalisation problems.(4) Generalized problems of discrete Tsirelson equations, in particular, those taking values in compact groups, and those of Markov chains evolving according to a road coloring.
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[Remarks] Kouji Yano, Application of Ito's excursion theory to limit theorems, Research Arena, vol.2 no.1, 1-2, Kobe University, 2009.
