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The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues

   
@article{EJP793,
	author = {Kohei Uchiyama},
	title = {The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {15},
	year = {2010},
	keywords = {asymptotic formula, Green function, random walk of zero mean and finite variances, absorption on a line},
	abstract = {We obtain asymptotic estimates of the Green functions of random walks on the two-dimensional integer lattice that are killed on the horizontal axis. A basic asymptotic formula whose leading term is virtually the same as the explicit formula for the corresponding Green function of Brownian motion is established under the existence of second moments only. Some refinement of it is given under a slightly stronger moment condition. The extension of the results to random walks on the higher dimensional lattice is also given.},
	pages = {no. 37, 1161-1189},
	issn = {1083-6489},
	doi = {10.1214/EJP.v15-793},    
        url = {http://ejp.ejpecp.org/article/view/793}}