The expansion of the criticality theory for stochastic optimal control and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04935
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Aoyama Gakuin University
• Principal Investigator: ICHIHARA Naoyuki 青山学院大学, 理工学部, 准教授 (70452563)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 確率最適制御

Outline of Final Research Achievements

In this research, we studied the criticality theory for a class of nonlinear partial differential equations, called viscous Hamilton-Jacobi equations, by using both probabilistic and PDE theoretic methods. More specifically, we clarified the relationship between “phase transition” phenomena arising in stochastic optimal control and the generalized principal eigenvalue for viscous Hamilton-Jacobi equations. We especially quantified such phase transitions in terms of the space dimensions as well as the intensity of nonlinearity of the equation.

Free Research Field

確率論