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Hamiltonian stochastic Lie systems and applications by de Lucas, J.; Rivas, X.; Zajac, M. is a scholarly article available to read on EtoBox.

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This paper provides a practical approach to stochastic Lie systems, i.e. stochastic differential equations whose general solutions can be written as a function depending only on a generic family of particular solutions and some constants, so as to emphasise their applications. We correct the known stochastic Lie theorem characterising stochastic Lie systems, proving that, contrary to previous claims, it satisfies the Malliavin's principle. Meanwhile, we show that stochastic Lie systems admit new stochastic features in the Ito approach. New generalisations of stochastic Lie systems, like the so-called stochastic foliated Lie systems, are devised. Subsequently, we focus on stochastic (foliated) Lie systems that can be studied as Hamiltonian systems using different types of differential geometric structures. We study their stability properties and we devise the basics of an energy-momentum method. A stochastic Poisson coalgebra method is developed to derive superposition rules for Hamiltonian stochastic Lie systems. Applications of our results are found in coronavirus stochastic models, stochastic Lotka-Volterra systems, stochastic SIS models of different types, etc. Our results impro

Author

de Lucas, J.; Rivas, X.; Zajac, M.

Published

2023

Language

EN