| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
1. The Brascamp-Lieb inequality has importance in statistical mechanics, such as in the analysis of interface models. We give a simple proof of the inequality based on stochastic analysis; as an application of our method, also derived are error estimates of the inequality and its extensions to nonconvex potentials.
2. We recover the principle terms in asymptotic estimates for tail probabilities of first hitting times of Bessel process in a relatively simple manner based on the weak convergence of probability measures; sharp asymptotics of remainder terms are also derived.
3. We clarify sufficient conditions for expectations of the Feynman-Kac type with singular potentials to diverge in the following three cases: Brownian motion, symmetric stable process, and Brownian motion in the half-space with singular potentials on the boundary.
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