Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

Giuseppe Gaeta; Roma Kozlov; Francesco Spadaro; Giuseppe Gaeta; Roma Kozlov; Francesco Spadaro

doi:10.3934/mine.2022038

Mathematics in Engineering

2022, Volume 4, Issue 5: 1-52. doi: 10.3934/mine.2022038

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Research article

Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

1.
Dipartimento di Matematica, Università degli Studi di Milano, v. Saldini 50, 20133 Milano, Italy
2.
SMRI, Santa Marinella, Italy
3.
Department of Business and Management Science, Norwegian School of Economics, Helleveien 30, N-5045, Bergen, Norway
4.
EPFL, CSFT, SB, Batiment MA - Station 8, CH-1015 Lausanne, Switzerland

Received: 02 August 2021 Accepted: 13 September 2021 Published: 08 October 2021

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.
- symmetry,
- stochastic differential equations,
- asymptotic properties,
- conserved quantities,
- invariance
Citation: Giuseppe Gaeta, Roma Kozlov, Francesco Spadaro. Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations[J]. Mathematics in Engineering, 2022, 4(5): 1-52. doi: 10.3934/mine.2022038

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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.

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