1. Un principe d'invariance pour une classe de marches p-corrélées sur ℤd
- Author
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Alexis Bienvenüe, Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon
- Subjects
Statistics and Probability ,[SHS.STAT]Humanities and Social Sciences/Methods and statistics ,Markov chain ,Characteristic function (probability theory) ,Function space ,Covariance matrix ,General Mathematics ,010102 general mathematics ,Function (mathematics) ,16. Peace & justice ,Space (mathematics) ,Random walk ,01 natural sciences ,Combinatorics ,010104 statistics & probability ,Limit (mathematics) ,0101 mathematics ,Statistics, Probability and Uncertainty ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let ζ be a Markov chain on a finite state space D, f a function from D to ℝd, and Sn = ∑k=1nf(ζk). We prove an invariance theorem for S and derive an explicit expression of the limit covariance matrix. We give its exact value for p-reinforced random walks on ℤ2 with p = 1, 2, 3.
- Published
- 1998
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