Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

  title={Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations},
  author={Giuseppe Gaeta and Roman Kozlov and Francesco Spadaro},
  journal={Mathematics in Engineering},
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 classification of scalar autonomous Ito stochastic differential equations with simple noise

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.



Asymptotic symmetries and asymptotically symmetric solutions of partial differential equations

  • G. Gaeta
  • 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.

Symmetries of stochastic differential equations: A geometric approach

A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of

Random Lie-point symmetries of stochastic differential equations

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,

Recent advances in symmetry of stochastic differential equations.

We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the

Integration of the stochastic logistic equation via symmetry analysis

  • G. Gaeta
  • Mathematics
    Journal of Nonlinear Mathematical Physics
  • 2019
We apply the recently developed theory of symmetry of stochastic differential equations to a stochastic version of the logistic equation, obtaining an explicit integration, i.e. an explicit formula

Lie-point symmetries and stochastic differential equations: II

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

Reduction and reconstruction of stochastic differential equations via symmetries

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented, and a natural definition of reconstruction, inspired by the

Symmetry and integrability for stochastic differential equations

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) &