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Symétries d'équations aux dérivées partielles apparaissant dans des modèles stochastiques

Abstract : Numerous phenomenons in physics or financial mathematics can be modelised by stochastic processes or "pseudo-stochastic" processes (this notion will be explained in this thesis). Here the subject will be some partial differential equations (EDP) related to this type of model.In order to find solutions for these equations from trivial solutions, the determination of symmetries is efficient.In 1971, B. Kent Harrison et Frank B. Estabrook introduced a method to determine the symmetries of EDP : from a system of partial differential equations, after possibly a change of variable and/or a change of unknown, it possible to express them as the vanishing of a familly of differential forms. An isovector is defined as a vector field of all the variables the Lie derivative of which leaves the differential ideal generated by the forms invariant.These last years, several equations were studied thanks to this method and the symmetries of numerous EDP was determined. The computations in all these cases leave appear a large degree of similarity among these examples.Thus with that in mind, a general framework for the calculus of the symmetries with this method is developed. Propositions and isovectors depending on the type of EDP and some results on the Lie algebra of isovectors have been obtained.
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Submitted on : Monday, May 23, 2022 - 12:22:27 PM
Last modification on : Tuesday, May 24, 2022 - 3:49:17 AM


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  • HAL Id : tel-03675698, version 1


Laurène Valade. Symétries d'équations aux dérivées partielles apparaissant dans des modèles stochastiques. Equations aux dérivées partielles [math.AP]. Normandie Université, 2021. Français. ⟨NNT : 2021NORMR088⟩. ⟨tel-03675698⟩



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