Development of Method of Heun's Differential Equation in Applied Stochastic Processes

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K11993
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: University of Tsukuba
• Principal Investigator: KONNO Hidetoshi 筑波大学, システム情報系(名誉教授), 名誉教授 (20134207)
• Research Collaborator: TAMURA Yoshiyasu ; PASZIT Imre
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 応用確率過程解析 / ホインの微分方程式 / 非平衡系の生成・死滅過程 / 非線形確率過程 / 長期記憶効果 / 位相特異点ダイナミクス / 複雑系のダイナミクス

Outline of Final Research Achievements

In the classical applied probability theory and analysis, mathematical analysis can be possible only when Markov stochastic models can be reduced to problems of solving Gauss’s hyper-geometric differential equation (GHGDE). In the present study, we developed `` a method of Heun’s differential equation (HDE)’’ to treat a class of non-Markov, non-Gaussian stochastic models which are related to solving problems beyond the class of GHGDE. The main theoretical methods covers for (1) solving a class of fractional master equation; (2) solving a class of fractional Fokker-Planck equation with third order nonlinear in the regression term and second order in the diffusion term; (3) generating superstatistical fractional Poisson process, a class of stochastic process beyond HDE. Applied examples in the real world are shown with their developed methods.

Free Research Field

確率論的リスク解析