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Representation of the characteristic function of a stochastic integral

Published online by Cambridge University Press:  14 July 2016

M. Riedel
M. Riedel*
Affiliation:
Karl Marx University, Leipzig
*
∗Postal address: Sektion Mathematik, Karl-Marx-Universität Leipzig, 701 Leipzig, Karl-Marx-Platz 10–12, GDR.
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Abstract

Let X(t) be a continuous, homogeneous stochastic process with independent increments characterized by a, σ, M, N in the Lévy representation formula. In this note we obtain the Lévy canonical representation of the characteristic function of a stochastic integral (in the sense of convergence in probability) of the form (where υ(t) is a non-decreasing, non-negative and left-continuous function) in terms of υ(t), a, σ, M, N.

Keywords

INFINITELY DIVISIBLE DISTRIBUTIONLÉVY CANONICAL REPRESENTATIONCONTINUOUSHOMOGENEOUS STOCHASTIC PROCESS WITH INDEPENDENT INCREMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 448 - 455
Copyright
Copyright © Applied Probability Trust 1980 

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References

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