Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-17T02:56:43.340Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Halmos, P. (1950) Measure Theory. Van Nostrand, New York.CrossRefGoogle Scholar
[2] Lukacs, E. (1970) Characteristic Functions, 2nd edn. Griffin, London.Google Scholar
[3] Lukacs, E. (1975) Stochastic Convergence, 2nd edn. Academic Press, New York.Google Scholar
[4] Robbins, H. (1948) Mixture of distributions. Ann. Math. Statist. 19, 360–369.CrossRefGoogle Scholar