The Eigenvalue Problem of Singular Ergodic Control |
| |
Authors: | Ryan Hynd |
| |
Institution: | Courant Institute, 251 Mercer Street, New York, NY 10012‐1185 |
| |
Abstract: | We consider the problem of finding a real number λ and a function u satisfying the PDE Here f is a convex, superlinear function. We prove that there is a unique λ* such that the above PDE has a viscosity solution u satisfying $\lim_{|x|\rightarrow \infty}u(x)/|x|=1$ . Moreover, we show that associated to λ* is a convex solution u* with D2u*∈ $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}L^{\infty}(\R^N)$ and give two min‐max formulae for λ*. λ* has a probabilistic interpretation as being the least, long‐time averaged (ergodic) cost for a singular control problem involving f. © 2011 Wiley Periodicals, Inc. |
| |
Keywords: | |
|
|