Characterizing attraction probabilities via the stochastic Zubov equation. (English) Zbl 1123.60311
Summary: A stochastic differential equation with an a.s. locally stable compact set is considered. The attraction probabilities to the set are characterized by the sublevel sets of the limit of a sequence of solutions to 2nd order partial differential equations. Two numerical examples illustrating the method are presented.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93E15 | Stochastic stability in control theory |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
| 34F05 | Ordinary differential equations and systems with randomness |
