| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We studied infinite dimensional stochastic differential equations (ISDEs) representing infinite particles systems with long range interaction. We proved the existence and uniqueness of solutions of ISDEs for systems of interacting diffusion processes (joint work with H. Osada ). We generalized the result to systems of jump type process including Levy process (joint work with S. Esaki) and those of hard core balls. As an application of these results, we showed the uniqueness of Dirichlet forms associated the systems (joint work with Y. Kawamoto and H. Osada ).
We also studied on percolation models composed by sticks whose centers are arranged by a Poisson point process and directions are i. i. d. We examined the relation between the distribution of direction of sticks and the shape of cluster, and obtained a kind of phase transition (joint work with R. Roy).
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