Nonconventional large deviations theorems

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• 作者：Yuri Kifer (1)
  S. R. S. Varadhan (2)
  
• 关键词：Large deviations ; Markov processes ; Nonconventional averages ; Hyperbolic diffeomorphisms ; Primary 60F10 ; Secondary 60J05 ; 60J25 ; 37D20
• 刊名：Probability Theory and Related Fields
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：158
• 期：1-2
• 页码：197-224
• 全文大小：324 KB
• 作者单位：Yuri Kifer (1)
  S. R. S. Varadhan (2)
  
  1. Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel
  2. Courant Institute for Mathematical Studies, New York University, 251 Mercer St, New York, NY, 10012, USA
  
• ISSN：1432-2064

文摘

We obtain large deviations theorems for both discrete time expressions of the form $\sum _{n=1}^NF\big (X(q_1(n)),\ldots ,X(q_\ell (n))\big )$ and similar expressions of the form $\int _0^TF\big ( X(q_1(t)),\ldots , X(q_\ell (t))\big )dt$ in continuous time. Here $X(n),n\ge 0$ or $X(t), t\ge 0$ is a Markov process satisfying Doeblin’s condition, $F$ is a bounded continuous function and $q_i(n)=in$ for $i\le k$ while for $i>k$ they are positive functions taking on integer values on integers with some growth conditions which are satisfied, for instance, when $q_i$ ’s are polynomials of increasing degrees. Applications to some types of dynamical systems such as mixing subshifts of finite type and hyperbolic and expanding transformations will be obtained, as well.