%0 Report %T Regular Solutions of Second-Order Stationary Hamilton-Jacobi Equations %+ Mathematical Analysis and Numerical Simulation of Non-Linear Models (NUMATH) %A Gozzi, Fausto %A Rouy, Elisabeth %N RR-2649 %P 33 %I INRIA %8 1995 %D 1995 %K Hamilton-jacobi equations %K optimal stochastic control %K dynamic programming %K ito's formula %K infinite dimension %K maximal monotone operators %Z Computer Science [cs]/Other [cs.OH]Reports %X We study a second-order stationary Hamilton-Jacobi equation in infinite dimension. This equation is nonlinear and convex with respect to the first-ord- er term. We use properties of a the transition semigroup associated to the linear equation to write the Hamilton-Jacobi equation in integral form and we prove that this solution is the pointwise limit of a uniformly bounded sequence of classical solutions of approximating problems. Finally, the solution is the value function of the associated optimal stochastic control problem. Some examples are given. %G English %2 https://inria.hal.science/inria-00074041/document %2 https://inria.hal.science/inria-00074041/file/RR-2649.pdf %L inria-00074041 %U https://inria.hal.science/inria-00074041 %~ INRIA %~ INRIA-RRRT %~ INRIA-LORRAINE %~ INRIA-NANCY-GRAND-EST %~ TESTALAIN1 %~ INRIA2 %~ LARA