Urn-related Random Walk with Drift Ρ X
نویسندگان
چکیده
We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the walk, and show some interesting applications to Friedman’s urn, as well as showing the connection with Lamperti’s walk with asymptotically zero drift.
منابع مشابه
Urn - related random walk with drift ρ x α / t β
We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the walk, and show some interesting applications to Friedman’s urn, as well as showing the connection with Lamperti’s walk with asymptotically zero drift .
متن کاملUrn Models, Replicator Processes, and Random Genetic Drift
To understand the relative importance of natural selection and random genetic drift in finite but growing populations, the asymptotic behavior of a class of generalized Polya urns is studied using the method of ordinary differential equation (ODE). Of particular interest is the replicator process: two balls (individuals) are chosen from an urn (the population) at random with replacement and bal...
متن کاملTail Asymptotics for the Maximum of Perturbed Random Walk
Stanford University Consider a random walk S = (Sn : n ≥ 0) that is “perturbed” by a stationary sequence (ξn : n ≥ 0) to produce the process (Sn + ξn : n ≥ 0). This paper is concerned with computing the distribution of the all-time maximum M∞ = max{Sk + ξk : k ≥ 0} of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including product...
متن کاملLocal probabilities for random walks with negative drift conditioned to stay nonnegative∗
Let {Sn, n ≥ 0} with S0 = 0 be a random walk with negative drift and let τx = min {k > 0 : Sk < −x} , x ≥ 0. Assuming that the distribution of the i.i.d. increments of the random walk is absolutely continuous with subexponential density we describe the asymptotic behavior, as n→∞, of the probabilities P (τx = n) and P(Sn ∈ [y, y+ ∆), τx > n) for fixed x and various ranges of y. The case of latt...
متن کاملOn the survival of a class of subcritical branching processes in random environment
Let Zn be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let X be the logarithm of the expected offspring size per individual given the environment. Assuming that the density of X has the form pX(x) = x −β−1 l0(x)e −ρx for some β > 2, a slowly varying function l0(x) and ρ ∈ (0, 1) , we find the asymptotic survival probabil...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007