On nonlinear elliptic Bellman systems for a class of stochastic differential games in arbitrary dimension
| Type of publication: | Article |
| Citation: | |
| Publication status: | Published |
| Journal: | Mathematical Models and Methods in Applied Sciences |
| Volume: | 21 |
| Number: | 1 |
| Year: | 2011 |
| Pages: | 215--240 |
| Note: | NCMM Preprint no. 2010-015 |
| URL: | http://www.karlin.mff.cuni.cz/... |
| DOI: | 10.1142/S0218202511005027 |
| Abstract: | We consider nonlinear elliptic Bellman systems which arise in the theory of stochastic differential games. The right-hand sides of the equations (which are called Hamiltonians) may have quadratic growth with respect to the gradient of the unknowns. Under certain assumptions on the Hamiltonians, that are satisfied for many types of stochastic games, we establish the existence of a regular solution. This partially generalizes recent works of Bensoussan, Frehse and Vogelgesang from two-dimensional setting onto arbitrary dimension. The main novelty of the paper consists of introducing a new (semi-continuity) method for obtaining the continuity of the solution and the corresponding estimates. |
| Keywords: | Bellman equation, Hamiltonians, nonlinear elliptic equations, regularity, semi-continuity method, Stochastic games |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
|
Attachments
|
|
|
Notes
|
|
|
|
|
|
Topics
|
|
|
|
