83 research outputs found
Gaussian estimates for spatially inhomogeneous random walks on
It is shown in this paper that the transition kernel corresponding to a
spatially inhomogeneous random walk on admits upper and lower
Gaussian estimates.Comment: Published at http://dx.doi.org/10.1214/009117905000000440 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Discrete harmonic functions on an orthant in Zd
International audienceWe give a positive answer to a conjecture on the uniqueness of harmonic functions in the quarter plane stated by K. Raschel. More precisely we prove the existence and uniqueness of a positive discrete harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed at the boundary of an orthant in Zd. Our methodsallow on the other hand to generalize from the quarter plane to orthants in higher dimensions and to treat the spatially inhomogeneous walks
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