Infinite ergodicity in generalized geometric ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift
Auteur(s) :
Giordano, Stefano [Auteur]
Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN [AIMAN-FILMS - IEMN]
Cleri, Fabrizio [Auteur]
Physique - IEMN [PHYSIQUE - IEMN]
Blossey, Ralf [Auteur]
Unité de Glycobiologie Structurale et Fonctionnelle - UMR 8576 [UGSF]
![refId](/themes/Mirage2//images/idref.png)
Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN [AIMAN-FILMS - IEMN]
Cleri, Fabrizio [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Physique - IEMN [PHYSIQUE - IEMN]
Blossey, Ralf [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Unité de Glycobiologie Structurale et Fonctionnelle - UMR 8576 [UGSF]
Titre de la revue :
Physical Review E
Pagination :
044111
Éditeur :
American Physical Society (APS)
Date de publication :
2023-04-17
ISSN :
2470-0045
Mot(s)-clé(s) en anglais :
Brownian motion
Stochastic processes
Statistical Physics
Stochastic processes
Statistical Physics
Discipline(s) HAL :
Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]
Science non linéaire [physics]
Science non linéaire [physics]
Résumé en anglais : [en]
Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g. in finance, in physics and biology. The definition of the process depends ...
Lire la suite >Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g. in finance, in physics and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter α with 0 ≤ α ≤ 1 , giving rise to the well-known special cases α = 0 (Itô), α = 1/2 (Fisk-Stratonovich) and α = 1 (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter α. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.Lire moins >
Lire la suite >Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g. in finance, in physics and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter α with 0 ≤ α ≤ 1 , giving rise to the well-known special cases α = 0 (Itô), α = 1/2 (Fisk-Stratonovich) and α = 1 (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter α. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Source :
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