Ergodic Problems for Viscous Hamilton--Jacobi Equations with Inward Drift | Zendy

Emmanuel Chasseigne | Zendy; Naoyuki Ichihara | Zendy

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Ergodic Problems for Viscous Hamilton--Jacobi Equations with Inward Drift

Author(s) -

Emmanuel Chasseigne,

Naoyuki Ichihara

Publication year - 2019

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/18m1179328

Subject(s) - ergodic theory , eigenfunction , mathematics , uniqueness , eigenvalues and eigenvectors , hamiltonian (control theory) , mathematical analysis , perturbation (astronomy) , hamilton–jacobi equation , mathematical physics , physics , mathematical optimization , quantum mechanics

In this paper we study the ergodic problem for viscous Hamilton--Jacobi equations with superlinear Hamiltonian and inward drift. We investigate (i) existence and uniqueness of eigenfunctions associated with the generalized principal eigenvalue of the ergodic problem, (ii) relationships with the corresponding stochastic control problem of both finite and infinite time horizon, and (iii) the precise growth exponent of the generalized principal eigenvalue with respect to a perturbation of the potential function.

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