## 28 Citations

Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

- MathematicsMathematics in Engineering
- 2022

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…

W-symmetries of backward stochastic differential equations, preservation of simple symmetries and Kozlov's theory

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2021

Symmetry and integrability for stochastic differential equations

- Mathematics
- 2017

We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A 43 (2010) &…

Lie Point Symmetries of Autonomous Scalar First-Order Itô Stochastic Delay Ordinary Differential Equations

- Mathematics
- 2021

In this paper, we consider an extension of Lie group theory to the class of constant delay autonomous stochastic differential equations of Ito form. The determining equations are deterministic even…

Lie symmetry reductions and integrability of approximated small delay stochastic differential equations

- Mathematics
- 2020

This paper presents Lie symmetries of small delay stochastic differential equations (SDSDE). We derive an approximation of a small delay stochastic differential equation (SDSDE) equivalence to a…

Lie group Method for Solving System of Stochastic Differential Equations

- MathematicsJournal of Physics: Conference Series
- 2020

In the current work, we realize Lie group method for system of stochastic differential equations(SDE). To comprehend this method which is used the vector field in the function and solved system by…

Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise

- Mathematics, Computer Science
- 2022

This work provides a classiﬁcation of scalar autonomous Ito stochastic dif-ferential equations with simple noise possessing symmetries, and extends previous classi ﬁcations in that it also considers recently introduced types of symmetry, in particular standard random symmetry, not considered in those.

Finite dimensional solutions to SPDEs and the geometry of infinite jet bundles

- Mathematics
- 2017

Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A…

Symmetry classification of scalar Ito equations with multiplicative noise

- MathematicsJournal of Nonlinear Mathematical Physics
- 2020

We provide a symmetry classification of scalar stochastic equations with multiplicative noise. These equations can be integrated by means of the Kozlov procedure, by passing to symmetry adapted…

On the geometry of twisted prolongations, and dynamical systems

- Mathematics
- 2018

I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.

## References

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Random Lie-point symmetries of stochastic differential equations

- Mathematics
- 2017

We study the invariance of stochastic differential equations under random diffeomorphisms and establish the determining equations for random Lie-point symmetries of stochastic differential equations,…

Solving stochastic differential equations with Cartan's exterior differential system

- Mathematics
- 2015

The aim of this work is to use systematically the symmetries of the (one dimensional) bacward heat equation with potentiel in order to solve certain one dimensional It\^o's stochastic differential…

Asymptotic symmetries and asymptotically symmetric solutions of partial differential equations

- Mathematics, Computer Science
- 1994

An approach to asymptotic symmetry based on the methods of Lie theory and the renormalization group approach recently proposed by Bricmont and Kupiainen for the Ginzburg-Landau equation is proposed.

Lie-point symmetries and stochastic differential equations: II

- Mathematics
- 2000

We complement the discussion of symmetries of Ito equations given in Gaeta and Rodriguez Quintero (1999 J. Phys. A: Math. Gen. 32 8485-505) by considering transformations acting on vector Wiener…

A Formal Approach for Handling Lie Point Symmetries of Scalar First-Order Itô Stochastic Ordinary Differential Equations

- Mathematics
- 2008

Abstract Many methods of deriving Lie point symmetries for Itô stochastic ordinary differential equations (SODEs) have surfaced. In the Itô calculus context both the formal and intuitive…

Normal Forms, symmetry, and linearization of dynamical systems

- Mathematics
- 2013

We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We…

Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries

- MathematicsEuropean Journal of Applied Mathematics
- 1990

An algorithm is presented to linearize nonlinear partial differential equations by non-invertible mappings. The algorithm depends on finding nonlocal symmetries of the given equations which are…

Nonlocal symmetries. Heuristic approach

- Mathematics
- 1991

A constructive method for constructing nonlocal symmetries of differential equations based on the Lie—Bäcklund theory of groups is developed. The concept of quasilocal symmetries is introduced. With…

Stochastic variational principles and quantum mechanics

- Mathematics
- 1988

The main purpose of this paper is to analyze the connections between the Eulerian and the Lagrangian approaches to stochastic variational principles. In particular, it will be shown how different…