Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations
| Autor: | Anthony Le Cavil, Nadia Oudjane, Francesco Russo |
|---|---|
| Přispěvatelé: | Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), EDF R&D (EDF R&D), EDF (EDF), Laboratoire de Finance des Marchés d'Energie (FiME Lab), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-CREST-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Optimisation et commande (OC), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), The third named author has benefited partially from thesupport of the ``FMJH Program Gaspard Monge in optimization and operationresearch' (Project 2014-1607H). |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Differential equation 65C05 65C35 68U20 60H10 60H30 60J60 58J35 01 natural sciences 010104 statistics & probability Stochastic differential equation FOS: Mathematics McKean type Non-linear Stochastic Differential Equations 0101 mathematics Mathematics Particle systems Partial differential equation Applied Mathematics 010102 general mathematics Mathematical analysis Nonlinear Partial Differential Equations Probability (math.PR) Chaos propagation 16. Peace & justice Probabilistic representation of PDEs Stochastic partial differential equation [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Nonlinear system Modeling and Simulation McKean–Vlasov process Mathematics - Probability Separable partial differential equation Numerical partial differential equations |
| Popis: | We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which we associate a random function which is proved to converge to a solution of a regularized version of a nonlinear PDE. arXiv admin note: substantial text overlap with arXiv:1504.03882 |
| Databáze: | OpenAIRE |
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