Martingale-difference Gibbs random fields and central limit theorem
نویسندگان
چکیده
منابع مشابه
The Martingale Central Limit Theorem
One of the most useful generalizations of the central limit theorem is the martingale central limit theorem of Paul Lévy. Lévy was in part inspired by Lindeberg’s treatment of the central limit theorem for sums of independent – but not necessarily identically distributed – random variables. Lindeberg formulated what, in retrospect, is the right hypothesis, now known as the Lindeberg condition,1...
متن کاملA Martingale Central Limit Theorem
We present a proof of a martingale central limit theorem (Theorem 2) due to McLeish (1974). Then, an application to Markov chains is given.
متن کاملCentral Limit Theorem for Random Fields
A new variant of CLT is established for random elds de ned on Rd which are strictly stationary, with nite second moment and weakly dependent (comprising cases of positive or negative association). The summation domains grow in the van Hove sense. Simultaneously the indices of observations form more and more dense grids in these domains. Thus the e ect of combining two scaling procedures is stud...
متن کاملA Central Limit Theorem for Random Fields
A central limit theorem is proved for α-mixing random fields. The sets of locations where the random field is observed become more and more dense in an increasing sequence of domains. The central limit theorem concerns these observations. The limit theorem is applied to obtain asymptotic normality of kernel type density estimators. It turns out that in our setting the covariance structure of th...
متن کاملThe Local Central Limit Theorem for a Gibbs Random Field
We extend the validity of the implication of a local limit theorem from an integral one. Our extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential. 1. Definitions and Results 1.1. Assumptions We consider a v-dimensional lattice spin system, to each χeZ is associated a spin sx that ...
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: Annales Academiae Scientiarum Fennicae Series A I Mathematica
سال: 1992
ISSN: 0066-1953
DOI: 10.5186/aasfm.1992.1714