Tohoku Mathematical Journal
2014
June
SECOND SERIES VOL. 66, NO. 2

Tohoku Math. J.
66 (2014), 289-307

Title GREEN'S FUNCTIONS OF RANDOM WALKS ON THE UPPER HALF PLANE

Author Kôhei Uchiyama

(Received February 8, 2013)
Abstract. We obtain an asymptotic estimate of the Green function of a random walk on $\boldsymbol{Z}^2$ having zero mean and killed when it exits from the upper half plane. A little more than the second moment condition is assumed. The estimate obtained is used to derive an exact asymptotic form of the hitting distribution of the lower half plane of the walk. The higher dimensional walks are dealt with in the same way.

Mathematics Subject Classification. Primary 60G50; Secondary 60J45.
Key words and phrases. Asymptotic formula, Green function, random walk of zero mean and finite variance, hitting probability of half plane.

To the top of this page

Back to the Contents