Analytic Solutions of Equation for Random Evolution on a Complex Plane
DOI:
https://doi.org/10.17713/ajs.v52iSI.1757Abstract
We discuss a generalization of Goldstein-Kac model on a complex plane and apply probabilistic approach to construct solutions of the corresponding Cauchy problem for complex-analytic initial conditions. The method is based on reconstruction of complex-
analytic functions by combination of power functions, for which corresponding solutions are the moments of evolution process.
As soon as in the hydrodynamic limit the equation for our model approximates a Schrödinger-type equation, the solutions constructed for pre-limit Cauchy problem may approximate solutions for corresponding Cauchy problem for a Schrödinger-type equation.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Igor Samoilenko, Ganna Verovkina, Tetiana Samoilenko
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
