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August, 1984 Additive Processes on Nuclear Spaces
A. S. Ustunel
Ann. Probab. 12(3): 858-868 (August, 1984). DOI: 10.1214/aop/1176993234


In this work we construct general additive processes on the nuclear spaces, and prove Khintchin's formula and Paul Levy's decomposition for these processes. As applications, we construct some Ornstein-Uhlenbeck processes with jumps and solve some (stochastic) partial differential equations obtained from the transformations of these processes by a random diffeomorphism corresponding to a finite dimensional diffusion process.


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A. S. Ustunel. "Additive Processes on Nuclear Spaces." Ann. Probab. 12 (3) 858 - 868, August, 1984.


Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0554.60072
MathSciNet: MR744240
Digital Object Identifier: 10.1214/aop/1176993234

Keywords: 46E , 46F , 60G , 60H , 81E , Additive processes , free quantum field , integration by parts formula , Levy's measure , Nuclear spaces , Ornstein-Uhlenbeck processes , Semimartingales , Stochastic flows

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • August, 1984
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