2021/02/27 by Amarjit Budhiraja, Budhiraja, Amarjit, Paul Dupuis +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F99 #60H10 #93E20 #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:60F99 #msc:60H10 #msc:93E20
paper · pdf · doi:10.48550/arxiv.2103.00280
arxiv created 2021/02/27 · openalex publication_date 2021/02/27 · arxiv updated 2021/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study the basic properties of two ergodic stochastic control problems associated with the quasistationary distribution (QSD) of a diffusion process X relative to a bounded domain. The two problems are in some sense dual, with one defined in terms of the generator associated with X and the other in terms of its adjoint. Besides proving wellposedness of the associated Hamilton-Jacobi-Bellman equations, we describe how they can be used to characterize important properties of the QSD. Of particular note is that the QSD itself can be identified, up to normalization, in terms of the cost potential of the control problem associated with the adjoint.