A Conditional Local Limit Theorem for Recurrent Random Walk
نویسندگان
چکیده
منابع مشابه
Central Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملThe Local Limit Theorem: A Historical Perspective
The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...
متن کاملCentral Limit Theorem for Excited Random Walk in the Recurrent Regime
Let Y = Z× (Z/LZ), where L > 1 is an integer, G = {−e1, e1,−e2, e2} where ej are coordinate vectors. We denote the coordinates of points y ∈ Y by (x(y), s(y)). Consider a cookie environment on Y, that is, for each y ∈ Y, j ∈ N, there is a probability distribution ω(y, j, e) on G. Consider an excited random walk Yn = (Xn, Sn) that is P(Yn+1 − Yn = e|Y1, . . . , Yn) = ω(Yn, ln, e) where ln is the...
متن کاملCentral Limit Theorem for the Excited Random Walk in Dimension
We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d ≥ 2.
متن کاملThe Local Central Limit Theorem for a Gibbs Random Field
We extend the validity of the implication of a local limit theorem from an integral one. Our extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential. 1. Definitions and Results 1.1. Assumptions We consider a v-dimensional lattice spin system, to each χeZ is associated a spin sx that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1975
ISSN: 0091-1798
DOI: 10.1214/aop/1176996276