Limit theorems for a random directed slab graph
نویسندگان
چکیده
منابع مشابه
Limit theorems for a random directed slab graph
We consider a stochastic directed graph on the integers whereby a directed edge between i and a larger integer j exists with probability pj−i depending solely on the distance between the two integers. Under broad conditions, we identify a regenerative structure that enables us to prove limit theorems for the maximal path length in a long chunk of the graph. The model is an extension of a specia...
متن کاملLimit Theorems for Random Walks with Boundaries
In this review, we consider boundary problems for random walks generated by sums of independent items and some of their generalizations. Let 1, 42, . . * be identically distributed independent random variables with distribution frunction F(x). Let S = 0, Sn = Sk= Ok with n = 1, 2, * -. We shall study the properties of the random trajectory formed by the sums S0, S1, 82, . Let n be an integer pa...
متن کاملLimit Theorems for Random Triangular Urn Schemes
In this paper we study a generalized Pólya urn with balls of two colors and a random triangular replacement matrix. We extend some results of Janson (2004), (2005) to the case where the largest eigenvalue of the mean of the replacement matrix is not in the dominant class. Using some useful martingales and the embedding method introduced in Athreya and Karlin (1968), we describe the asymptotic c...
متن کاملLimit Theorems for Sequences of Random Trees
We consider a random tree and introduce a metric in the space of trees to define the “mean tree” as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we show laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random tree...
متن کاملCentral Limit Theorems for Dependent Random Variables
1. Limiting distributions of sums of 'small' independent random variables have been extensively studied and there is a satisfactory general theory of the subject (see e.g. the monograph of B.V. Gnedenko and A.N. Kolmogorov [2]). These results are conveniently formulated for double arrays Xn k (k = 1, . . . , kn ; n = 1, 2, . . . ) of random variables where the Xn k (k = 1, . . . , kn), the rand...
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 Applied Probability
سال: 2012
ISSN: 1050-5164
DOI: 10.1214/11-aap783