Uniform convergence of exact large deviations for renewal reward processes
نویسندگان
چکیده
منابع مشابه
From uniform renewal theorem to uniform large and moderate deviations for renewal-reward processes
A uniform key renewal theorem is deduced from the uniform Blackwell’s renewal theorem. A uniform LDP (large deviation principle) for renewal-reward processes is obtained, and MDP (moderate deviation principle) is deduced under conditions much weaker than existence of exponential moments.
متن کاملUniform large and moderate deviations for functionalempirical processes
For fX i g i1 a sequence of i.i.d. random variables taking values in a Polish space with distribution , we obtain large and moderate deviation principles for the processes fn ?1 P nt] i=1 X i ; t 0g n1 and fn ?1=2 P nt] i=1 (X i ?); t 0g n1 , respectively. Given a class of bounded functions F on , we then consider the above processes as taking values in the Banach space of bounded functionals o...
متن کاملAsymptotics for renewal-reward processes with retrospective reward structure
Let {(Xi; Yi): i= : : : ;−1; 0; 1; : : :} be a doubly in nite renewal-reward process, where {Xi: i= : : :− 1; 0; 1; : : :} is an i.i.d. sequence of renewal cycle lengths and Yi= g(Xi−q; Xi−q+1; : : : ; Xi) is the lump reward earned at the end of the ith renewal cycle, with some function g :R q+1 → R . Starting with the rst renewal cycle (of duration X1) at the time origin, let C(t) denote the e...
متن کاملLarge Deviations for Stochastic Processes
The purpose of these lectures is to introduce you to the basics of large deviation theory. The emphasis will be on the use of compactness ideas (more extensive results are in Puhalskii [13]). Other approaches to large deviation theory are considered in Dembo and Zeitouni [3], den Hollander [4], Deuschel and Stroock [6], Dupuis and Ellis [7], Freidlin and Wentzell [9], Kallenberg [12], Shwartz a...
متن کاملLarge deviations for Wishart processes
Let X(δ) be a Wishart process of dimension δ, with values in the set of positive matrices of size m. We are interested in the large deviations for a family of matrix-valued processes {δ−1X t , t ≤ 1} as δ tends to infinity. The process X(δ) is a solution of a stochastic differential equation with a degenerate diffusion coefficient. Our approach is based upon the introduction of exponential mart...
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: 2007
ISSN: 1050-5164
DOI: 10.1214/105051607000000023