Introduction
My research interests are in the areas of probability theory and partial differential equations. I am particularly interested in deterministic and stochastic optimal control, Hamilton-Jacobi-Bellman equations, and Markov decision processes. My current research focuses on the study of principal eigenvalues for viscous Hamilton-Jacobi equations arising in stochastic calculus of variations.
Preprints
N. Ichihara and M. Iida, The vanishing discount limit for infinite horizon finite state Markov decision processes with constraints (submitted)
Research papers
E. Chasseigne and N. Ichihara, Sharp estimates of the generalized principal eigenvalue for superlinear viscous Hamilton-Jacobi equations with inward drift, Nonlinear Differential Equations Appl. NoDEA 29(4), Article:34 (2022) (article, final draft)
N. Ichihara, Convergence of value functions for finite horizon Markov decision processes with constraints, Appl. Math. Optim. 84(2) 2177-2220 (2021) (article, final draft)
N. Ichihara, Phase transitions arising in stochastic ergodic control associated with viscous Hamilton-Jacobi equations with bounded inward drift, SN Partial Differ. Equ. Appl. (2021) 2(1), Article:15 (article, final draft)
E. Chasseigne and N. Ichihara, Ergodic problems for viscous Hamilton-Jacobi equations with inward drift, SIAM J. Control Optim. 57(1) 23-52 (2019) (article, final draft)
E. Chasseigne and N. Ichihara, Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton-Jacobi equations, Nonlinear Differential Equations Appl. NoDEA 23(6), Article:66 (2016) (article, final draft)
N. Ichihara, Phase transitions for controlled Markov chains on infinite graphs, SIAM J. Control Optim. 54(2) 450-474 (2016) (article, final draft)
N. Ichihara, The generalized principal eigenvalue for Hamilton-Jacobi-Bellman equations of ergodic type, Ann. Inst. H. Poincaré Anal. Non Linéaire 32(3) 623–650 (2015) (article, final draft)
N. Ichihara, Criticality of viscous Hamilton-Jacobi equations and stochastic ergodic control, J. Math. Pures Appl. 100(3) 368-390 (2013) (article, final draft)
N. Ichihara and S.-J. Sheu, Large time behavior of solutions of Hamilton-Jacobi-Bellman equations with quadratic nonlinearity in gradients, SIAM J. Math. Anal. 45(1) 279-306 (2013) (article, final draft)
N. Ichihara, Large time asymptotic problems for optimal stochastic control with superlinear cost, Stochastic Process. Appl. 122(4) 1248-1275 (2012) (article, final draft)
N. Ichihara, Recurrence and transience of optimal feedback processes associated with Bellman equations of ergodic type, SIAM J. Control Optim. 49(5) 1938-1960 (2011) (article, final draft)
N. Ichihara and H. Ishii, Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians, Arch. Ration. Mech. Anal. 194(2) 383-419 (2009) (article, final draft)
N. Ichihara and H. Ishii, The large-time behavior of solutions of Hamilton-Jacobi equations on the real line, Methods Appl. Anal. 15(2) 223-242 (2008) (article, final draft)
N. Ichihara and H. Ishii, Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians, Comm. Partial Differential Equations 33(5) 784-807 (2008) (article, final draft)
N. Ichihara, A stochastic representation for fully nonlinear PDEs and its application to homogenization, J. Math. Sci. Univ. Tokyo 12(3) 467-492 (2005) (article, final draft)
N. Ichihara, Homogenization for stochastic partial differential equations derived from nonlinear filterings with feedback, J. Math. Soc. Japan 57(2) 593-603 (2005) (article, final draft)
R. Buckdahn and N. Ichihara, Limit theorem for controlled backward SDEs and homogenization of Hamilton-Jacobi-Bellman equations, Appl. Math. Optim. 51(1) 1-33 (2005) (article, final draft)
N. Ichihara, Homogenization problem for stochastic partial differential equations of Zakai type, Stoch. Stoch. Rep. 76(3) 243-266 (2004) (article, final draft)
Conference proceedings
N. Ichihara, A dynamical approach to asymptotic solutions of Hamilton-Jacobi equations, Proceedings of the International Conference for the 25th Anniversary of Viscosity Solution, pp.107-115 (2008)
N. Ichihara, Periodic homogenization of Hamilton-Jacobi-Bellman equations, Proceedings of the 11th International Symposium on Continuum Models and Discrete Systems, pp.119-124 (2008)
Others
N. Ichihara, Phase transitions arising in stochastic control and ergodic type HJB equations (Japanese), Systems, Control and Information Vol. 64, No. 7, pp. 246-251 (2020) (article)
N. Ichihara, Phase transitions for controlled Markov chains on infinite graphs, RIMS Kokyuroku No. 1952, pp.86-91 (2015)
N. Ichihara, Criticality of ergodic type HJB equations and stochastic ergodic control, RIMS Kokyuroku No. 1855, pp.109-114 (2013)
N. Ichihara, Long time asymptotic problems for stochastic optimal control and related variational problems, RIMS Kokyuroku No.1837, pp.102-113 (2013)
N. Ichihara, Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians, RIMS Kokyuroku No.1651, pp.137-160 (2009)
N. Ichihara, Asymptotic solutions of a class of Hamilton-Jacobi equations, RIMS Kokyuroku No.1545, pp.88-111 (2007)
N. Ichihara, Asymptotic solutions of Hamilton-Jacobi equations with non-periodic perturbations, RIMS Kokyuroku No.1542, pp.24-32 (2007)
N. Ichihara, Homogenization of fully nonlinear PDEs and backward SDEs, RIMS Kokyuroku No.1481, pp.20-31 (2006)