Local large deviations and the strong renewal theorem
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 کاملLocal limit theorem for large deviations and statistical box-tests
Abstract: Let n particles be independently allocated into N boxes, where the l-th box appears with the probability al. Let μr be the number of boxes with exactly r particles and μ = [μr1 , . . . , μrm ]. Asymptotical behavior of such random variables as N tends to infinity was studied by many authors. It was previously known that ifNal are all upper bounded and n/N is upper and lower bounded by...
متن کاملLarge Deviations and Strong Mixing
Résumé Nous prouvons le propriétés de grandes déviations (P.G.D.) pour les mesures empiriques en τ -topologie, dans les cas de suites stationnaires sous conditions de mélange α(n) exp(−n(log n)1+δ) pour certain δ > 0, ou φ(n) exp(−n`(n)) avec `(n)→∞. Les examples de châınes de Markov récurrentes au sense de Doeblin montrent que ces conditions ne permettrent pas de amélioration substantielle, et...
متن کاملLocal Large Deviations, McMillian Theorem for multitype Galton-Watson Processes
Abstract. In this article we prove a local large deviation principle (LLDP) for the critical multitype Galton-Watson process from spectral potential point. We define the so-called a spectral potential UK( ·, π) for the Galton-Watson process, where π is the normalized eigen vector corresponding to the leading Perron-Frobenius eigen value 1l of the transition matrix A(·, ·) defined from K, the tr...
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 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: Electronic Journal of Probability
سال: 2019
ISSN: 1083-6489
DOI: 10.1214/19-ejp319