Abstract
For a controlled stochastic differential equation with a finite horizon cost functional, a necessary condition for optimal control of degenerate diffusions with non-smooth coefficients is derived. The main idea is to show that the SDE admits a unique linearized version interpreted as its distributional derivative with respect to the initial condition. We use a technique of Bouleau-Hirsch on absolute continuity of probability measures in order to define the adjoint process on an extension of the initial probability space.
| Original language | English |
|---|---|
| Pages (from-to) | 37-54 |
| Number of pages | 18 |
| Journal | Random Operators and Stochastic Equations |
| Volume | 17 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 2009 |
| Externally published | Yes |
Bibliographical note
Funding Information:First author: Partially supported by PHC Tassili 07 MDU 705. Third author: Partially supported by PHC Tassili 07 MDU 705.
Keywords
- Maximum principle
- Non-smooth coefficients
- Optimal control
- Stochastic differential equation
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
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