Local limit theorem in deterministic systems
نویسندگان
چکیده
On montre que dans tout système dynamique probabilisé ergodique et apériodique, il existe une fonction de carré intégrable à valeurs entières dont les sommes Birkhoff satisfont le théorème limite local.
منابع مشابه
The Local Limit Theorem: A Historical Perspective
The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...
متن کاملCentral Limit Theorem for Deterministic Systems
A unified approach to obtaining the central limit theorem for hyperbolic dynamical systems is presented. It builds on previous results for one dimensional maps but it applies to the multidimensional case as well. CONTENT 0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p. 2 1. A general probabilistic result . . . . ....
متن کاملCENTRAL LIMIT THEOREM FOR DETERMINISTIC SYSTEMSCarlangelo
A uniied approach to obtaining the central limit theorem for hyperbolic dynamical systems is presented. It builds on previous results for one dimensional maps but it applies to the multidimensional case as well.
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملA Local Limit Theorem for Random Walks in Balanced Environments
Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems — yielding a Gaussian density multiplied by a highly oscillatory modulating factor — for such models have been obtained. In the one-dimensional nearest-neighbor case with i.i.d. transition probabilities, local limits of uni...
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 de l'I.H.P
سال: 2022
ISSN: ['0246-0203', '1778-7017']
DOI: https://doi.org/10.1214/21-aihp1169