Geodesic
On the dynamic programming principle for controlled diffusion processes in a cylindrical region
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 302-310

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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 controlled process.
Keywords: dynamic programming principle, exit time, value function, semicontinuity. 
@article{SEMR_2013_10_a20,
     author = {D. B. Rokhlin},
     title = {On the dynamic programming principle for controlled diffusion processes in a cylindrical region},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {302--310},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a20/}
}
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D. B. Rokhlin. On the dynamic programming principle for controlled diffusion processes in a cylindrical region. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 302-310. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a20/