| Budget Amount *help |
¥13,520,000 (Direct Cost: ¥10,400,000、Indirect Cost: ¥3,120,000)
Fiscal Year 2013: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2012: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2011: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
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| Research Abstract |
The theory of Dirichlet forms has been developed as a useful tool for studying symmetric Markov processes. The theory of Dirichlet forms is an L-2-theory, and which is a reason why the theory is suitable for treating singular Markov processes. However, the theory of Markov processes is, in a sense, an L-1-theory. To bridge this gap, we prove the L-p-independence of growth bounds of Markov semi-groups under the conditions for the Markov processes to be strong Feller and to be tight. By applying the L-p-independence to time changed Markov processes, we show the exponential integrability of positive continuous additive functionals (PCAF's in short) and the large deviation principle of PCAF's. Moreover, we give a necessary and sufficient condition for heat kernel estimates being stable by perturbation of potential terms.
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