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Seminari / Kozlov

Martedì 5 marzo ore 14:30 Aula C


R. Kozlov (NHH Bergen)


parlerà di

"On symmetries of stochastic differential equations"


Abstract: Lie point symmetries of Ito stochastic differential equations (SDEs) are considered. They correspond to Lie group transformations of the independent variable (time) and dependent variables, which preserve the differential form of the SDEs and properties of the Brownian motion.

In the considered framework transformations of the Brownian motion aregenerated by the random time change.

There are provided some properties of the SDEs symmetries: the symmetries form a Lie algebra, there are relations between the symmetries and the first integrals, and for some classes of SDEs there are results on maximal dimensionality of the admitted symmetry algebras.

The symmetries can be used to construct Lie symmetry group classifications and to integrate SDEs with the help of quadratures. The relation to symmetries of the associated Fokker-Planck (FP) equation is also mentioned.



Giovedì 7 marzo ore 14:30 Aula C


R. Kozlov (NHH Bergen)


parlerà di

“The adjoint equation method for constructing first integrals of difference equations”


Abstract:A new method for finding first integrals of discrete equations is presented.

It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation.

The method is based on a newly established identity which links symmetries of the underlying discrete equations, solutions of the discrete adjoint equations and first integrals. The method can be applied to invariant mappings (discrete equations) and to discretizations of ordinary differential equations. If a sufficient number of first integrals can be obtained, it is possible to find the general solution of the discrete equations.



27 febbraio 2019
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