We consider a locally non-homogeneous discrete-time random walk on Z, with the non-homogeneous perturbation concentrated at the origin. We assume exponential decay of the probabilities and symmetry for the homogeneous term. Combining probabilistic and analytic methods, we find an explicit expression for the asymptotic behavior of the probabilities P(X-t = x vertical bar X-0 = 0), as t -> infinity, which holds uniformly for x = o(t(3/4)). We also discuss the probabilistic interpretation of the results.

Random Walk on Z with One-Point Inhomogeneity / Boldrighini, Carlo; A., Pellegrinotti. - In: MARKOV PROCESSES AND RELATED FIELDS. - ISSN 1024-2953. - STAMPA. - 18:(2012), pp. 421-440.

Random Walk on Z with One-Point Inhomogeneity

BOLDRIGHINI, Carlo;
2012

Abstract

We consider a locally non-homogeneous discrete-time random walk on Z, with the non-homogeneous perturbation concentrated at the origin. We assume exponential decay of the probabilities and symmetry for the homogeneous term. Combining probabilistic and analytic methods, we find an explicit expression for the asymptotic behavior of the probabilities P(X-t = x vertical bar X-0 = 0), as t -> infinity, which holds uniformly for x = o(t(3/4)). We also discuss the probabilistic interpretation of the results.
2012
local central limit theorem; inhomogeneous random walk; random walk; central limit theorem; non-homogeneous random walk
01 Pubblicazione su rivista::01a Articolo in rivista
Random Walk on Z with One-Point Inhomogeneity / Boldrighini, Carlo; A., Pellegrinotti. - In: MARKOV PROCESSES AND RELATED FIELDS. - ISSN 1024-2953. - STAMPA. - 18:(2012), pp. 421-440.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/493175
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