Bellman–Isaacs equations of ergodic type related to risk‐sensitive control and their singular limits

Article type: Research Article

Authors: Kaise, Hidehiro | Nagai, Hideo^;

Affiliations: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, 560, Japan E‐mail: kaise@sigmath.es.osaka‐u.ac.jp | Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, 560, Japan E‐mail: nagai@sigmath.es.osaka‐u.ac.jp

Note: [] Research supported in part by Grant‐in‐Aid for Scientific Research No. 08640280, the Ministry of Education, Science and Culture.

Abstract: Bellman–Isaacs equation of ergodic type is studied in paricular case. A solution of the equation related to the principal eigenfunction of the Schrödinger operator is obtained as the limit of the solution of a Bellman–Isaacs equation of discounted type. Furthermore, a singular limit of the equation is studied in relation to semi‐classical analysis.

Journal: Asymptotic Analysis, vol. 16, no. 3-4, pp. 347-362, 1998