Displaying similar documents to “On the survival probability of a branching process in a random environment”

Limit laws of transient excited random walks on integers

Elena Kosygina, Thomas Mountford (2011)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

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...

Asymptotics for the survival probability in a killed branching random walk

Nina Gantert, Yueyun Hu, Zhan Shi (2011)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope − , where denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when → 0, this probability decays like exp{−(+o(1)) / 1/2}, where is a positive constant...

Transience/recurrence and the speed of a one-dimensional random walk in a “have your cookie and eat it” environment

Ross G. Pinsky (2010)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

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...