Ergodic BSDE with an unbounded and ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Ergodic BSDE with an unbounded and multiplicative underlying diffusion and application to large time behavior of viscosity solution of HJB equation
Auteur(s) :
Hu, Ying [Auteur correspondant]
Institut de Recherche Mathématique de Rennes [IRMAR]
Lemonnier, Florian [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Institut de Recherche Mathématique de Rennes [IRMAR]
Lemonnier, Florian [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Titre de la revue :
Stochastic Processes and their Applications
Pagination :
4009-4050
Éditeur :
Elsevier
Date de publication :
2019
ISSN :
0304-4149
Mot(s)-clé(s) en anglais :
multiplicative and unbounded diffusion
ergodic backward stochastic differential equation
HJB equation
large time behavior
rate of convergence
ergodic backward stochastic differential equation
HJB equation
large time behavior
rate of convergence
Discipline(s) HAL :
Mathématiques [math]/Probabilités [math.PR]
Résumé en anglais : [en]
In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward ...
Lire la suite >In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward process has an unbounded diffusion is balanced with an assumption of weak dissipativity for its drift. Moreover, the forward equation is assumed to be non-degenerate. Like in [HMR15], we show that the solution of a BSDE in finite horizon T behaves basically as a linear function of T, with a shift depending on the solution of the associated EBSDE, with an explicit rate of convergence. Finally, we apply our results to an ergodic optimal control problem. In particular, we show the large time behaviour of viscosity solution of Hamilton-Jacobi-Bellman equation with an exponential rate of convergence when the undelrying diffusion is multiplicative and unbounded.Lire moins >
Lire la suite >In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward process has an unbounded diffusion is balanced with an assumption of weak dissipativity for its drift. Moreover, the forward equation is assumed to be non-degenerate. Like in [HMR15], we show that the solution of a BSDE in finite horizon T behaves basically as a linear function of T, with a shift depending on the solution of the associated EBSDE, with an explicit rate of convergence. Finally, we apply our results to an ergodic optimal control problem. In particular, we show the large time behaviour of viscosity solution of Hamilton-Jacobi-Bellman equation with an exponential rate of convergence when the undelrying diffusion is multiplicative and unbounded.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
Collections :
Source :
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- http://arxiv.org/pdf/1801.01284
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- https://hal.archives-ouvertes.fr/hal-01674766/document
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- EBSDE_unbounded.pdf
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- 1801.01284
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