An asymptotic expansion for the distribution of the supremum of a random walk

M. Sgibnev

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Displaying similar documents to “An asymptotic expansion for the distribution of the supremum of a random walk”

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We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the – suitably centered – empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov, see (1984) 491–506. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time...

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Consider a variant of the simple random walk on the integers, with the following transition mechanism. At each site , the probability of jumping to the right is ()∈[½, 1), until the first time the process jumps to the left from site , from which time onward the probability of jumping to the right is ½. We investigate the transience/recurrence properties of this process in both deterministic and stationary, ergodic environments {()}∈. In deterministic environments, we also study the speed...

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We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, , is larger than 1 then ERW is transient to the right and, moreover, for >4 under the averaged measure it obeys the Central Limit Theorem. We show that when ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited...

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