Abstract
In this paper we continue our study of a multidimensional random walk with zero mean and finite variance killed on leaving
a cone.We suggest a new approach that allows one to construct a positive harmonic function in Lipschitz cones under minimal moment
conditions. This approach allows also to obtain more accurate information about the behaviour of the harmonic function not far from
the boundary of the cone. We also prove limit theorems under new moment conditions.
a cone.We suggest a new approach that allows one to construct a positive harmonic function in Lipschitz cones under minimal moment
conditions. This approach allows also to obtain more accurate information about the behaviour of the harmonic function not far from
the boundary of the cone. We also prove limit theorems under new moment conditions.
| Original language | English |
|---|---|
| Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
| Publication status | Accepted/In press - 2 Oct 2022 |
Keywords
- Random walk
- exit time
- harmonic function
- conditioned process