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On the Mean of a Stochastic Integral with Non-Gaussian α-Stable Noise.
- Source :
- Stochastic Analysis & Applications; Mar/Apr2009, Vol. 27 Issue 2, p258-269, 12p
- Publication Year :
- 2009
-
Abstract
- In this article, we consider a Levy process under condition Γ1 = x where {Γk} is a sequence of arrivals of a Poisson process with unit arrival rate. We show that under condition Γ1 = x Levy process can be decomposed into a simple process and a Levy process. These two processes are independent. As an application of this decomposition we consider α-stable Levy processes. We give a closed form of the process [image omitted] and evaluate its expected value where Z is an α-stable Levy process with 0 < α < 2. We show that X(t) = 0 for 1 < α < 2 and this expectation is equal infinity for α ≤ 1. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 07362994
- Volume :
- 27
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Stochastic Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 36623943
- Full Text :
- https://doi.org/10.1080/07362990802558337