2011 Fiscal Year Final Research Report
On asymptotic behaviors of stochastic processes in random environments and properties of random environments
| Project/Area Number |
21540144
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
TAMURA Yozo 慶應義塾大学, 理工学部, 教授 (50171905)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAGAWA Hironobu 慶應義塾大学, 理工学部, 講師 (60348810)
SUZUKI Yuki 慶應義塾大学, 医学部, 講師 (30286645)
MAEJIMA Makoto 慶應義塾大学, 理工学部, 名誉教授 (90051846)
SASADA Makiko 慶應義塾大学, 理工学部, 助教 (00609042)
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| Co-Investigator(Renkei-kenkyūsha) |
TANAKA Hiroshi 慶應義塾大学, 理工学部, 名誉教授 (70011468)
ATSUJI Atsushi 慶應義塾大学, 経済学部, 教授 (00221044)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 確率論 |
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| Research Abstract |
On asymptotic behaviors of stochastic processes in random environments, mainly the recurrence properties of diffusion processes in multi-dimensional random environments are investigated. As discontinuous random environments, those having the form of sums of 1-dimensional stable processes are treated and as continuous random environments, multi-dimensional Gaussian random environments are considered. The recurrence properties of diffusion processes in those environments are proved. To investigate long time asymptotic behaviors of diffusions in more general environments, the large deviation principle for long time behaviors of current corresponding to stochastic integral is obtained with explicit rate function. On the properties of random environments, mainly some characterizations of self-decomposable distributions are given.
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