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Title: 超過程の生存性とモデルへの応用 (第13回生物数学の理論とその応用 : 連続および離散モデルのモデリングと解析)
Other Titles: Survival Property for Superprocesses and Its Application to Models (Theory of Biomathematics and its Applications XIII : Modeling and Analysis for Discrete and Continuous Models)
Authors: 道工, 勇  KAKEN_name
Author's alias: Dôku, Isamu
Issue Date: Sep-2017
Publisher: 京都大学数理解析研究所
Journal title: 数理解析研究所講究録 = RIMS Kokyuroku
Volume: 2043
Start page: 6
End page: 12
Abstract: 本研究では, ガン細胞に対する免疫応答を記述する環境依存型の確率モデルを考察する. 数理的には, 単純な離散モデルから出発して, 適当なスケール変換則の下での極限操作により連続型モデルに移行し, 出現する確率過程の性質を論じる. 特に生存性に関連して, モデル過程の生存確率の近似評価式に基づくことにより, 初期値依存で結果が異なる状況が出現する, いわゆる創始者支配となる様相を呈する状況について詳しく解析する.
In the present article we consider an environment-dependent stochastic model which describes the immune response against cancer cells. Mathematically, starting from a simple discrete model, we will derive a continuous type model by limit procedure under a suitable scaling and discuss some properties of the derived stochastic process. In particular, in connection with the survival property of the process, we derive an approximate estimate formula for survival probability of the model process. Based upon the formula, we shall precisely analyze the so-called founder control phase, namely, the situation that distinct results follow according to the different initial conditions.
URI: http://hdl.handle.net/2433/236949
Appears in Collections:2043 Theory of Biomathematics and its Applications XIII : Modeling and Analysis for Discrete and Continuous Models

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