Renewal Theorem for a Class of Stationary Sequences
نویسنده
چکیده
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 construction.
منابع مشابه
On the existence of nonnegative solutions for a class of fractional boundary value problems
In this paper, we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation. By applying Kranoselskii`s fixed--point theorem in a cone, first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function. Then the Arzela--Ascoli theorem is used to take $C^1$ ...
متن کاملA non-linear Renewal Theorem with stationary and slowly changing perturbations
Abstract: Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the excess over a boundary, and an expansion for the expected first passage time. The formulation is motivated by problems in sequential analysis with sta...
متن کاملIEOR 6711 : Introduction to Renewal Theory II
Here we will present some deeper results in renewal theory such as a central limit theorem for counting processes, stationary versions of renewal processes, renewal equations, the key renewal theorem, weak convergence. 1 Central limit theorem for counting processes Consider a renewal process {t n : n ≥ 1} with iid interarrival times X n = t n − t n−1 , n ≥ 0, such that 0 < E(X) = 1/λ < ∞ and 0 ...
متن کاملA Tauberian theorem for $(C,1,1)$ summable double sequences of fuzzy numbers
In this paper, we determine necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a double sequence of fuzzy numbers follows from its $(C,1,1)$ summability. These conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. We also construct some interesting double sequences of fuzzy numbers.
متن کاملShortcut Node Classification for Membrane Residue Curve Maps
comNode classification within Membrane Residue Curves (M-RCMs) currently hinges on Lyapunov’s Theorem and therefore the computation of mathematically complex eigenvalues. This paper presents an alternative criterion for the classification of nodes within M-RCMs based on the total membrane flux at node compositions. This paper demonstrates that for a system exhibiting simple permeation behaviour...
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 1986