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

TL;DR

This paper proves the dynamic programming principle for controlled diffusion processes within a cylindrical region, assuming standard conditions and a nonnegative integrand in the functional to be maximized.

Contribution

It establishes the dynamic programming principle for controlled diffusions in a cylindrical domain under minimal assumptions and standard SDE conditions.

Findings

Proves the DPP for controlled diffusions in cylindrical regions.

Ensures existence of a unique strong solution for the SDE.

Validates the DPP under nonnegative integrand and standard assumptions.

Abstract

We prove the dynamic programming principle for a class of diffusion processes controlled up to the time of exit from a cylindrical region $[0,T)\times G$. 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.