Miguel Abadi and Nicolas Vergne 2008 Nonlinearity 21 2871 doi:10.1088/0951-7715/21/12/008
Sharp errors for point-wise Poisson approximations in mixing processes
Miguel Abadi1 and Nicolas Vergne2
Show affiliationsRecommended by K M Khanin
We describe the statistics of the number of occurrences of a string of symbols in a stochastic process: taking a string A of length n, we prove that the number of visits to A up to time t, denoted by Nt, has approximately a Poisson distribution. We provide a sharp error for this approximation. In contrast to previous works which present uniform error terms based on the total variation distance, our error is point-wise. As a byproduct we obtain that all the moments of Nt are finite. Moreover, we obtain explicit approximations for all of them. Our result holds for processes that verify the 
-mixing condition. The error term is explicitly expressed as a function of the rate function and is easily computable.
- PACS
- MSC
-
60F05 Central limit and other weak theorems
37A50 Relations with probability theory and stochastic processes (See also 60Fxx and 60G10)
- Subjects
- Dates
-
Issue 12 (December 2008)
Received 18 February 2008, in final form 12 September 2008
Published 19 November 2008
-
Sharp errors for point-wise Poisson approximations in mixing processes
Miguel Abadi and Nicolas Vergne 2008 Nonlinearity 21 2871
Users also read
What's this?- Vortex dynamics models in flow control problems
- The period function of hyperelliptic Hamiltonians of degree 5 with real critical points
- Positive-entropy geodesic flows on nilmanifolds
Related review articles
What's this?- Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory
- Dimension of non-conformal repellers: a survey
- Progress in normal form theory