Occupation time fluctuations of Poisson and equilibrium branching systems in critical and large dimensions

• Autorzy: Miłoś P.
• Języki publikacji: EN

Abstrakty

EN

Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in R^d with symmetric α-stable motion starting off from either a standard Poisson random field or the equilibrium distribution for critical d = 2α and large d > 2α dimensions. The limit processes are generalised Wiener processes. The obtained convergence is in space-time and finite-dimensional distributions sense. Under the additional assumption on the branching law we obtain functional convergence.

Słowa kluczowe

EN

functional central limit theorem; occupation time fluctuations; branching particles systems; generalised Wiener process; equilibrium distribution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2008
• Tom: Vol. 28, Fasc. 2
• Strony: 235--256
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Miłoś P.

• Insitute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, Warsaw, Poland

Bibliografia

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