We consider a class of ergodic Hamilton–Jacobi–Bellman (HJB) equations related to long-time asymptotics of nonsmooth multiplicative functional of diffusion processes. Under suitable ergodicity assumptions on the underlying diffusion, we show existence of these asymptotics and that they solve the related HJB equation in the viscosity sense.
A constructive approach to a class of ergodic HJB equations with nonsmooth cost
DAI PRA, PAOLO;
2008
Abstract
We consider a class of ergodic Hamilton–Jacobi–Bellman (HJB) equations related to long-time asymptotics of nonsmooth multiplicative functional of diffusion processes. Under suitable ergodicity assumptions on the underlying diffusion, we show existence of these asymptotics and that they solve the related HJB equation in the viscosity sense.
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