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Research Article | Open Access

Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

Giuseppe Gaeta1,2( ), Roma Kozlov3, Francesco Spadaro4
Dipartimento di Matematica, Università degli Studi di Milano, v. Saldini 50, 20133 Milano, Italy
SMRI, Santa Marinella, Italy
Department of Business and Management Science, Norwegian School of Economics, Helleveien 30, N-5045, Bergen, Norway
EPFL, CSFT, SB, Batiment MA - Station 8, CH-1015 Lausanne, Switzerland
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Abstract

We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.

Keywords

symmetrystochastic differential equationsasymptotic propertiesconserved quantitiesinvariance

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Mathematics in Engineering
Volume 4 Issue 5,
October 2022
Pages 1-52
DOI: 10.3934/mine.2022038

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Cite this article:
Gaeta G, Kozlov R, Spadaro F. Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations. Mathematics in Engineering, 2022, 4(5): 1-52. https://doi.org/10.3934/mine.2022038

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Received: 02 August 2021
Accepted: 13 September 2021
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)