Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physical Review E Année : 2023

Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift

Résumé

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.
Fichier principal
Vignette du fichier
Infinite_ergodicity_in_generalized_geometric_Brownian_motions_with_nonlinear_drift.pdf (648.22 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY ND - Paternité - Pas de modifications

Dates et versions

hal-04086877 , version 1 (02-05-2023)

Identifiants

Citer

Stefano Giordano, Fabrizio Cleri, Ralf Blossey. Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift. Physical Review E , 2023, 107 (4), pp.044111. ⟨10.1103/PhysRevE.107.044111⟩. ⟨hal-04086877⟩
18 Consultations
52 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More