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A Strong Law of Large Numbers for Super-stable Processes. Open Access

Descriptions

Author or creator
Kouritzin, Michael
Ren, Y.-X.
Additional contributors
Subject/Keyword
robability measures
super-Brownian motion
Fourier transform
vague convergence
strong law of large numbers
super-stable process
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
Let ℓ be Lebesgue measure and X=(Xt,t≥0;Pμ) be a supercritical, super-stable process corresponding to the operator −(−Δ)α/2u+βu−ηu2 on Rd with constants β,η>0 and α∈(0,2]. Put View the MathML source, which for each smallθ is an a.s. convergent complex-valued martingale with limit View the MathML source say. We establish for any starting finite measure μ satisfying View the MathML source that View the MathML source-a.s. in a topology, termed the shallow topology, strictly stronger than the vague topology yet weaker than the weak topology, where cα>0 is a known constant. This result can be thought of as an extension to a class of superprocesses of Watanabe’s strong law of large numbers for branching Markov processes.
Date created
2014
DOI
doi:10.7939/R35J32
License information
Rights
© 2014 Stochastic Processes and their Applications. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
Citation for previous publication
M. A. Kouritzin and Y-X. Ren. (2014), " A Strong Law of Large Numbers for Super-stable Processes '', Stochastic Processes and their Applications, 124, pp. 505-521.
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