Infinite ergodicity in generalized geometric ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift
Author(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]
Journal title :
Physical Review E
Pages :
044111
Publisher :
American Physical Society (APS)
Publication date :
2023-04-17
ISSN :
2470-0045
English keyword(s) :
Brownian motion
Stochastic processes
Statistical Physics
Stochastic processes
Statistical Physics
HAL domain(s) :
Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]
Science non linéaire [physics]
Science non linéaire [physics]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
Source :
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