Liu, Huili (2013) Some support properties for a class of LambdaFlemingViot processes. PhD thesis, Concordia University.

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Abstract
Using Donnelly and Kurtz's lookdown construction, we prove that the LambdaFlemingViot process with underlying Brownian motion has a compact support at any fixed time provided that the associated Lambdacoalescent comes down from infinity not too slowly. We also find both upper and lower bounds on Hausdorff dimension for the support at any fixed time. When the associated Lambdacoalescent has a nontrivial Kingman component, the Hausdorff dimension for the support is exactly two at any fixed time.
For such a LambdaFlemingViot process, we further prove a onesided modulus of continuity result for the ancestry process recovered from Donnelly and Kurtz's lookdown construction. As an application, we can prove that its support process also has the onesided modulus of continuity (with modulus function C\sqrt{tlog(1/t)}) at any fixed time.
In addition, we obtain that the support process is compact simultaneously at all positive times, and given the initial compactness, its range is uniformly compact over time interval [0,t) for all t>0.
Under a mild condition on the Lambdacoalescence rates, we also find a uniform upper bound on Hausdorff dimension for the support and an upper bound on Hausdorff dimension for the range.
Divisions:  Concordia University > Faculty of Arts and Science > Mathematics and Statistics 

Item Type:  Thesis (PhD) 
Authors:  Liu, Huili 
Institution:  Concordia University 
Degree Name:  Ph. D. 
Program:  Mathematics 
Date:  15 February 2013 
Thesis Supervisor(s):  Zhou, Xiaowen 
ID Code:  977144 
Deposited By:  HUILI LIU 
Deposited On:  17 Jun 2013 19:13 
Last Modified:  18 Jan 2018 17:43 
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