| Budget Amount *help |
¥15,730,000 (Direct Cost: ¥12,100,000、Indirect Cost: ¥3,630,000)
Fiscal Year 2018: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
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| Outline of Final Research Achievements |
We conducted research on Markov processes using stochastic analysis methods for cases of various state spaces, such as Euclid space, Riemannian manifold, and infinite dimensional space such as Wiener space and path space. In the case of the one-dimensional diffusion process, the spectrum of the Kolmogorov diffusion process was determined in the framework of supersymmetry. Also, in the case of Kummer process, spectra were determined in Zygmundt space or Orlicz space.
Furthermore, we characterized the ultracontractivity using the asymmetric Dirichlet form and applied to the asymptotic behavior of the fundamental solution in the case of compact Riemannian manifolds. We also constructed a non-symmetric diffusion process on the Wiener space as a typical example of an infinite dimensional space.
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