| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
I studied the continuity in the initial value and the parameter of the density component of the transition probability density function of the solutions to stochastic differential equations with non-regular coefficients, and obtained the Hoelder continuity in the initial value under a very weak assumption on the coefficients. Moreover, I obtained the continuity which is the almost same level as that of the equation without drift term in the parameter of the density component under a weak asummption on the coefficients. The continuity of the transition probability density function is associated with the continuity in the space parameters of the fundamental solutions to second-order parabolic partial differential equations. Besides, I also obtained some results on the recurrence of the Brownian motion in random environments, and on the convergence of the distributions of random variables by Malliavin calculus and Stein's method.
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