Weak convergence of mutually independent $Xₙ^B$ and $Xₙ^A$ under weak convergence of $Xₙ ≡ Xₙ^B - Xₙ^A$

• Autorzy: W. Szczotka
• Języki publikacji: EN

Abstrakty

EN

For each n ≥ 1, let ${v_{n,k}, k ≥ 1}$ and ${u_{n,k}, k ≥ 1}$ be mutually independent sequences of nonnegative random variables and let each of them consist of mutually independent and identically distributed random variables with means v̅ₙ and u̅̅ₙ, respectively. Let $Xₙ^B(t) = (1/cₙ) ∑_{j=1}^{[nt]}(v_{n,j} - v̅ₙ)$, $Xₙ^A(t) = (1/cₙ)∑_{j=1}^{[nt]}(u_{n,j}-u̅̅ₙ)$, t ≥ 0, and $Xₙ = Xₙ^B - Xₙ^A$. The main result gives conditions under which the weak convergence $Xₙ \mathrel{\mathop {\rightarrow}\limits^{𝓓}}X$, where X is a Lévy process, implies $Xₙ^B \mathrel{\mathop{\rightarrow}\limits^{𝓓}}X^B$ and $Xₙ^A\mathrel{\mathop{\rightarrow}\limits^{𝓓}}X^A$, where $X^B$ and $ X^A$ are mutually independent Lévy processes and $X = X^B - X^A$.

Kategorie tematyczne

• 60F15: Strong theorems
• 60F05: Central limit and other weak theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2006
• Tom: 33
• Numer: 1
• Strony: 41-49

Daty

wydano

2006

Twórcy

autor

W. Szczotka

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/am33-1-3