| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
We generalized a proof of existence of hydrodynamic limits and propagation of chaos of the stochastic ranking processes, to the cases of spatially dependent intensities for the point processes which determine the move-to-front (jump-to-top) random times. The processes are particle systems which mathematically model the rankings on the web, such as sales ranks of online bookstores, and the models give mathematical basis for the analysis of so called long-tail structure of online retails. The spatial dependence of intensities correspond to appeal effect of top sales. From mathematical point of view, introduction of spatial dependence on the intensity functions is a non-trivial perturbation, leading to continuum limits described in terms of the point processes with last-arrival-time dependent intensities.
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