| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
We give the joint distribution of the hitting time and site of a Brownian motion with and without constant drift. This result yields the formula for the expected volume of the Wiener sausages of Brownian motions and their asymptotic behavior for large time. Moreover we obtain the asymptotics of tail probabilities of first hitting times of Bessel processes with and without the drift. In addition, we find that zeros of Bessel function of the second kind are holomorhic with respect to the indices and establish the method of their calculation with a general-purpose computer soft of computations, Mathematica for example.
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