We consider a stochastic optimal control problem in the whole space, where the corresponding HJB equation is degenerate, with a quadratic running cost and coeffcients with linear growth. In this paper we provide a full mathematical details on the key estimate relating the asymptotic behavior of the solution as the space variable goes to infinite.
Numerical Analysis and Computation
Iourtchenko, D.V., Menaldi, J.-L. & Bratus, A.S. Nonlinear Differ. Equ. Appl. (2010) 17: 527. doi: 10.1007/s00030-010-0066-1