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Weak convergence to isotropic complex [Formula: see text] random measure.

Jun Wang¹, Yunmeng Li², Liheng Sang¹

¹School of Mathematics and Finance, Chuzhou University, Chuzhou, 239000 People's Republic of China.

Journal of Inequalities and Applications

|October 10, 2017

Summary

This study shows complex symmetric alpha-stable random measures can be approximated using a Poisson process-based complex process. This finding advances random measure approximation techniques in stochastic analysis.

Keywords:

Poisson processes complex [Formula: see text] random measure isotropic weak convergence

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Area of Science:

Stochastic Analysis
Random Measures
Complex Processes

Background:

Complex symmetric alpha-stable random measures are important in various fields.
Approximation methods for these measures are crucial for theoretical and applied research.

Purpose of the Study:

To demonstrate the approximation of isotropic complex symmetric alpha-stable random measures.
To introduce a novel approximation method using a Poisson process-based complex process.

Main Methods:

We utilized integrals based on a Poisson process with random intensity.
The core of the method involves constructing a complex process for approximation.

Main Results:

We proved that the complex process accurately approximates the target random measure.
The approximation holds for isotropic complex symmetric alpha-stable random measures.

Conclusions:

The proposed complex process offers a viable method for approximating alpha-stable random measures.
This work contributes to the understanding of random measure theory and its applications.