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January 2000 Hilbert space regularity of the $(\alpha,d,1)$-superprocess and its occupation time
D. Blount, A. Bose
Ann. Probab. 28(1): 104-131 (January 2000). DOI: 10.1214/aop/1019160113


The superprocess and its occupation time process are represented as Hilbert space valued solutions of stochastic evolution equations by using the Fourier transform of the process. For appropriate parameter values, the existence of density valued solutions follows. Pathwise regularity of the processes is obtained.As a new tool we develop a maximal inequality. We also extend the Tanaka-like evolution equations developed for local time processes and provide an Ito formula for certain functionals of the superprocess.


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D. Blount. A. Bose. "Hilbert space regularity of the $(\alpha,d,1)$-superprocess and its occupation time." Ann. Probab. 28 (1) 104 - 131, January 2000.


Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60031
MathSciNet: MR1755999
Digital Object Identifier: 10.1214/aop/1019160113

Primary: 60617 , 60G20 , 60G57 , 60H15

Keywords: Occupation times , Sobolev space regularity , stochastic evolution equation , Superprocess

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 1 • January 2000
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