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統計数学セミナー
過去の記録 ～10/06｜次回の予定｜今後の予定 10/07～
| 担当者 | 吉田朋広、増田弘毅、荻原哲平、小池祐太 |
|---|---|
| 目的 | 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う. |
2026年10月16日(金)
15:00-16:00 数理科学研究科棟(駒場) 128号室
ハイブリッド開催
Krzysztof Bartoszek 氏 (Department of Computer and Information Science, Linköping University)
An introduction to quadratic stochastic operators (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/JjtHEBHOT6m4SvmAcXrtWQ
ハイブリッド開催
Krzysztof Bartoszek 氏 (Department of Computer and Information Science, Linköping University)
An introduction to quadratic stochastic operators (English)
[ 講演概要 ]
Markov chains are inherently linear processes and also are not elegant for describing interactions between agents. For this end, non-linear models are needed, and quadratic stochastic operators (QSOs) are a first step. They describe mixing of two populations, e.g., sexual reproduction, where one parent comes from the female class and the other from the male class. Studying the law, even in the limit, of a population evolving under a QSO is a challenging task due to the interaction component between the two classes of individuals. Restricting the class of QSOs, to the so-called centred quadratic stochastic operators, one is able to show that, in the case of hermaphroditic species, when the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits, one can represent the law of the trait in descendant populations through an appropriate sum of independent random variables. QSOs can be further generalized to an arbitrary number of parents, and cubic stochastic operators are the next step.
[ 参考URL ]Markov chains are inherently linear processes and also are not elegant for describing interactions between agents. For this end, non-linear models are needed, and quadratic stochastic operators (QSOs) are a first step. They describe mixing of two populations, e.g., sexual reproduction, where one parent comes from the female class and the other from the male class. Studying the law, even in the limit, of a population evolving under a QSO is a challenging task due to the interaction component between the two classes of individuals. Restricting the class of QSOs, to the so-called centred quadratic stochastic operators, one is able to show that, in the case of hermaphroditic species, when the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits, one can represent the law of the trait in descendant populations through an appropriate sum of independent random variables. QSOs can be further generalized to an arbitrary number of parents, and cubic stochastic operators are the next step.
https://u-tokyo-ac-jp.zoom.us/meeting/register/JjtHEBHOT6m4SvmAcXrtWQ
