On the asymptotic behavior of the sequence and series of running maxima from a real random sequence
| Autor: | Rita Giuliano Antonini, Andrei Volodin, Thuntida Ngamkham |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
Sequence Running maxima of random variables Almost sure convergence phi-subgaussian random variables Series (mathematics) Continuous mapping theorem Random sequence Combinatorics Convergence of random variables Chain sequence Statistics Probability and Uncertainty Positive and negative parts Maxima Mathematics |
| Zdroj: | Statistics & Probability Letters. 83:534-542 |
| ISSN: | 0167-7152 |
| DOI: | 10.1016/j.spl.2012.10.010 |
| Popis: | For a sequence { X n , n ≥ 1 } of random variables, set Y n = max 1 ≤ k ≤ n X k − a n , where { a n , n ≥ 1 } is a sequence of constants to be specified. We obtain the limiting behavior of the sequences of positive and negative parts of { Y n , n ≥ 1 } when the tail distribution of { X n , n ≥ 1 } satisfies suitable “exponential-type” conditions. Next, we consider the rate convergence of the positive part to zero (results similar to complete convergence). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect