Modèles stochastiques lagrangiens de type McKean-Vlasov conditionnel et leur confinement PDF Download
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Author: Jean-François Jabir
Publisher:
ISBN:
Category :
Languages : en
Pages : 175
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Book Description
In this thesis, we are interested in theoretical aspects related to a new class of stochastic differential equations referred as Lagrangian stochastic models. These models have been introduced to model the properties of particles issued from turbulent flows. Motivated by a recent application of the Lagrangien models to the context of downscaling methods for weather forecasting, we also consider the introduction of boundary conditions in the dynamics. In the frame of nonlinear McKean equations, the Lagrangian stochastic models provide a particular case of non-linear dynamics due to the presence ion the coefficients of conditional distribution. For simplified cases, we establish a well-posedness result and particle approximations. In concern of boundary conditions, we construct a confined stochastic system within general domain for the prototypic “mean no-permeability” condition. In the case where the confinement domain is the hyper plane, we obtain existence and uniqueness results for the considered dynamics, and prove the accuracy of our model. For more general domains, we study the conditional McKean-Vlasov-Fokker-Planck equation satisfied by the law of the systems. We develop the notions of super- and sub-Maxwellians solutions, ensuring the existence of Gaussian bounds for the solution of the equation.
Author: Jean-François Jabir
Publisher:
ISBN:
Category :
Languages : en
Pages : 175
Get Book Here
Book Description
In this thesis, we are interested in theoretical aspects related to a new class of stochastic differential equations referred as Lagrangian stochastic models. These models have been introduced to model the properties of particles issued from turbulent flows. Motivated by a recent application of the Lagrangien models to the context of downscaling methods for weather forecasting, we also consider the introduction of boundary conditions in the dynamics. In the frame of nonlinear McKean equations, the Lagrangian stochastic models provide a particular case of non-linear dynamics due to the presence ion the coefficients of conditional distribution. For simplified cases, we establish a well-posedness result and particle approximations. In concern of boundary conditions, we construct a confined stochastic system within general domain for the prototypic “mean no-permeability” condition. In the case where the confinement domain is the hyper plane, we obtain existence and uniqueness results for the considered dynamics, and prove the accuracy of our model. For more general domains, we study the conditional McKean-Vlasov-Fokker-Planck equation satisfied by the law of the systems. We develop the notions of super- and sub-Maxwellians solutions, ensuring the existence of Gaussian bounds for the solution of the equation.
