The Annals of Probability

Additive Processes on Nuclear Spaces

A. S. Ustunel

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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.

Article information

Source
Ann. Probab., Volume 12, Number 3 (1984), 858-868.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993234

Digital Object Identifier
doi:10.1214/aop/1176993234

Mathematical Reviews number (MathSciNet)
MR744240

Zentralblatt MATH identifier
0554.60072

JSTOR
links.jstor.org

Keywords
60G 60H 46E 46F 81E Nuclear spaces additive processes Levy's measure integration by parts formula semimartingales Ornstein-Uhlenbeck processes free quantum field stochastic flows

Citation

Ustunel, A. S. Additive Processes on Nuclear Spaces. Ann. Probab. 12 (1984), no. 3, 858--868. doi:10.1214/aop/1176993234. https://projecteuclid.org/euclid.aop/1176993234


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