Limit theorems for a class of critical superprocesses with stable branching |
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Institution: | 1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK;2. CIMAT A. C., Calle Jalisco s/n, Col. Valenciana, A. P. 402, C.P. 36000, Guanajuato, Gto., Mexico;1. Istituto per le Applicazioni del Calcolo, CNR, Roma, Italy;2. Dipartimento di Informatica, Università di Torino, Italy;3. Dipartimento di Elettronica, Politecnico di Torino, Italy |
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Abstract: | We consider a critical superprocess with general spatial motion and spatially dependent stable branching mechanism with lowest stable index . We first show that, under some conditions, converges to 0 as and is regularly varying with index . Then we show that, for a large class of non-negative testing functions , the distribution of , after appropriate rescaling, converges weakly to a positive random variable with Laplace transform |
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Keywords: | Critical superprocess Stable branching Scaling limit Intrinsic ultracontractivity Regular variation |
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