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KAKEN_26400146seika.pdf
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Download
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:85.1 KB
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:Oct 31, 2019 |
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Total downloads since Oct 31, 2019 : 176
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| Title |
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確率順位付け模型とウェブランキングへの応用
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| Kana |
カクリツ ジュンイズケ モケイ ト ウェブ ランキング エノ オウヨウ
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Kakuritsu jun'izuke mokei to webu rankingu eno ōyō
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Stochastic ranking process and its applications to web ranking
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服部, 哲弥
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ハットリ, テツヤ
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Hattori, Tetsuya
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慶應義塾大学・経済学部 (日吉)・教授
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Research team head
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科研費研究者番号 : 10180902
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2019
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科学研究費補助金研究成果報告書
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2018
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ウェブで見られるランキングの時間発展のモデルとなる確率順位付け模型の位置強度結合経験分布の大数の法則 (流体力学極限) と軌道についてのカオスの伝搬の証明を，強度 (先頭に跳ぶ確率を与える点過程を定める関数) が位置依存性を持つ場合に一般化した．この一般化は，極限を記述する点過程の強度が直前の到着時刻に依存する非独立増分であるなど，強度が位置依存性を持たない場合の非自明な摂動問題である．確率順位付け模型はネット書店の売上順位の時間変化のモデルで，ロングテール構造の数理解析の基礎模型となる．強度の位置依存性は好順位の注目効果を意味する．
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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研究種目 : 基盤研究(C)(一般)
研究期間 : 2014～2018
課題番号 : 26400146
研究分野 : 数物系科学
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