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Article Dans Une Revue Symmetry Année : 2020

Toward a Wong-Zakai approximation for big order generators

Résumé

We give a new approximation with respect of the traditional parametrix method of the solution of a parabolic equation whose generator is of big order and under the Hoermander form. This generalizes to a higher order generator the traditional approximation of Stratonovitch diffusion which put in relation random ordinary differential equation (the leading process is random and of finite energy. When a trajectory of it is chosen, the solution of the equation is defined) and stochastic differential equation (the leading process is random and only continuous and we cannot choose a path in the solution which is only almost surely defined). We consider simple operators where the computations can be fully performed. This approximation fits with the semi-group only and not for the full path measure in the case of a stochastic differential equation.
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Dates et versions

hal-03212113 , version 1 (29-04-2021)

Identifiants

Citer

Rémi Léandre. Toward a Wong-Zakai approximation for big order generators. Symmetry, 2020, 12 (11), pp.1893. ⟨10.3390/sym12111893⟩. ⟨hal-03212113⟩
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