- Tytuł:
- On the central limit theorem for some birth and death processes
- Autorzy:
- Chojecki, Tymoteusz
- Powiązania:
- https://bibliotekanauki.pl/articles/747125.pdf
- Data publikacji:
- 2011
- Wydawca:
- Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
- Tematy:
-
Central limit theorem
Markov chain
Lamperti’s problem
birth and death processes
Kipnis-Varadhan theory
spectral gap - Opis:
- Suppose that \(\{Xn: n \geq 0\}\) is a stationary Markov chain and \(V\) is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if \(Y_n :=N^{-1/2}\sum_{n=0}^N V (X_n)\) converge in law to a normal random variable, as \(N \to+\infty\). For a stationary Markov chain with the \(L^2\) spectral gap the theorem holds for all \(V\) such that \(V (X_0)\) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables \(V\) for which the CLT holds for a class of birth and death chains whose dynamics has no spectral gap, so that Gordin’s result cannot be used and the result follows from an application of Kipnis-Varadhan theory.
- Źródło:
-
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2011, 65, 1
0365-1029
2083-7402 - Pojawia się w:
- Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł