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)