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A note on stochastic processes with independent increments taking values in an abelian group

Published online by Cambridge University Press:  14 July 2016

M.S. Bingham*
Affiliation:
University of Sheffield

Extract

It is well known that any stochastically continuous real valued stochastic process with independent increments defined on a compact time interval can be decomposed into a sum of independent processes, one of which is Gaussian with continuous sample paths, and the remainder of which have sample paths which are continuous except at a finite number of points with the discontinuities occurring at Poisson time points. The purpose of this note is to announce a proof of the above theorem in the case where the process takes values in an abelian group G. The detailed proof will appear elsewhere. The basic ideas of the proof in the case when G is finite dimensional Euclidean space are contained in Chapter VI of Gikhman and Skorohod (1965).

Type
Short Communications
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

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