Stochastic ranking process and its applications to web ranking
| Project/Area Number |
26400146
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Keio University |
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Principal Investigator |
HATTORI Tetsuya 慶應義塾大学, 経済学部(日吉), 教授 (10180902)
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| 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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| Keywords | 確率論 / 数理科学 / 確率過程論 / 大数の法則 / 流体力学極限 / 粒子系 / 確率順位付け模型 / 流体力学的極限 |
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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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| Academic Significance and Societal Importance of the Research Achievements |
急速な発達によって時代を特徴付けるに至った計算機とネットワーク環境によって，インターネット小売業のような大規模なアイテムの人気度の全順位がリアルタイムで更新される現象が可視化されオンライン中古市場のように経済的な意味を持つ時代に，実際のデータと現象の対応する数学的な方程式を「細いがまっすぐな道でつなぐ」こと（末節をそぎ落とした論理的中核の抽出）に成功した．世界的に例のない独自の研究である．最終的に到達した強度の位置依存性効果は，ランキングデータ自体の宣伝効果を与えるもので，数学的に精密で非自明な結果であり，将来技術が追いついてきたときに前もって筋の良い理屈を用意できていることを意味する．
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Report
(5 results)
Research Products
(9 results)
