منابع مشابه
Convergence Rates in the Implicit Renewal Theorem on Trees
R D = f(Ci, Ri, 1 ≤ i ≤ N), where f(·) is a possibly random real valued function, N ∈ {0, 1, 2, 3, . . . } ∪ {∞}, {Ci}i∈N are real valued random weights and {Ri}i∈N are iid copies of R, independent of (N,C1, C2, . . . ); D = represents equality in distribution. In the recent paper [10], an Implicit Renewal Theorem was developed that enables the characterization of the power tail asymptotics of ...
متن کاملOn the rate of convergence in the Kesten renewal theorem*
We consider the stochastic recursion Xn+1 = Mn+1Xn +Qn+1 on R , where (Mn, Qn) are i.i.d. random variables such that Qn are translations, Mn are similarities of the Euclidean space R. Under some standard assumptions the sequence Xn converges to a random variable R and the law ν of R is the unique stationary measure of the process. Moreover, the weak limit of properly dilated measure ν exists, d...
متن کاملConvergence rates in the local renewal theorem
We study subgeometric convergence rates in the local renewal theorem, which plays an important role in obtaining results on convergence rates for Markov chains [4]. Let {ξn}n≥0 and {ξ ′ n}n≥0 be two sequences of mutually independent and integervalued r.v.’s. Assume further that (i) ξ0 and ξ ′ 0 are non-negative r.v.’s; (ii) all {ξn}n≥1 and {ξ ′ n}n≥1 are i.i.d. and strictly positive, with a com...
متن کاملThe Key Renewal Theorem for a Transient Markov Chain
provided Eξ1 is finite and positive (see, for example, Feller and Orey [8], Feller [7, Ch. XI], Woodroofe [25, Appendix]); F is called lattice if it is concentrated on some lattice {ka, k ∈ Z} with a > 0. If F is lattice the same is true when h is a multiple of the span a. It is proved in Wang and Woodroofe [23] and in Borovkov and Foss [5, Theorem 2.6] that (1) holds uniformly over certain cla...
متن کاملRenewal Theorem for a Class of Stationary Sequences
A renewal theorem is obtained for stationary sequences of the form ~,=~( . . . , Xn_ ~, X,, X,+I , ...), where X,, n~Z, are i.i.d.r.v.s, valued in a Polish space. This class of processes is sufficiently broad to encompass functionals of recurrent Markov chains, functionals of stationary Gaussian processes, and functionals of one-dimensional Gibbs states. The theorem is proved by a new coupling ...
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: Kodai Mathematical Journal
سال: 1956
ISSN: 0386-5991
DOI: 10.2996/kmj/1138843770