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Scaling limits of branching random walks and branching-stable processes

Published online by Cambridge University Press:  04 August 2022

Jean Bertoin*
Affiliation:
University of Zurich
Hairuo Yang*
Affiliation:
University of Zurich
*
*Postal address: Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.
*Postal address: Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.

Abstract

Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanisms for point processes. Here we are interested in their domains of attraction and describe explicit conditions for a branching random walk to converge after a proper magnification to a branching-stable process. This contrasts with deep results obtained during the past decade on the asymptotic behavior of branching random walks and which involve either shifting without rescaling, or demagnification.

Type
Original Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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