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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

Abstract

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. https://doi.org/10.1214/aop/1176993234

Information

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

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Vol.12 • No. 3 • August, 1984
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