On the dynamic programming principle for controlled diffusion processes in a cylindrical region

2012/12/10 by Dmitry B. Rokhlin, Rokhlin, Dmitry B.
Economics, Econometrics and Finance · Mathematics · #60J60 #93E20 #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stochastic processes and financial applications #advanced mathematical theories #math.OC #msc:60J60 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1212.2191

9 pages

arxiv created 2012/12/10 · openalex publication_date 2012/12/10 · arxiv updated 2012/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the dynamic programming principle for a class of diffusion processes controlled up to the time of exit from a cylindrical region [0,T)× G. It is assumed that the functional to be maximized is in the Lagrange form with nonnegative integrand. Besides this we only adopt the standard assumptions, ensuring the existence of a unique strong solution of a stochastic differential equation for the state process.

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