# The ODE method for some self-interacting diffusions on ℝd

Annales de l'I.H.P. Probabilités et statistiques (2010)

- Volume: 46, Issue: 3, page 618-643
- ISSN: 0246-0203

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topKurtzmann, Aline. "The ODE method for some self-interacting diffusions on ℝd." Annales de l'I.H.P. Probabilités et statistiques 46.3 (2010): 618-643. <http://eudml.org/doc/243319>.

@article{Kurtzmann2010,

abstract = {The aim of this paper is to study the long-term behavior of a class of self-interacting diffusion processes on ℝd. These are solutions to SDEs with a drift term depending on the actual position of the process and its normalized occupation measure μt. These processes have so far been studied on compact spaces by Benaïm, Ledoux and Raimond, using stochastic approximation methods. We extend these methods to ℝd, assuming a confinement potential satisfying some conditions. These hypotheses on the confinement potential are required since in general the process can be transient, and is thus very difficult to analyze. Finally, we illustrate our study with an example on ℝ2.},

author = {Kurtzmann, Aline},

journal = {Annales de l'I.H.P. Probabilités et statistiques},

keywords = {self-interaction diffusion; reinforced processes; stochastic approximation; self-interacting diffusion; reinforced process; stochastic differential equation},

language = {eng},

number = {3},

pages = {618-643},

publisher = {Gauthier-Villars},

title = {The ODE method for some self-interacting diffusions on ℝd},

url = {http://eudml.org/doc/243319},

volume = {46},

year = {2010},

}

TY - JOUR

AU - Kurtzmann, Aline

TI - The ODE method for some self-interacting diffusions on ℝd

JO - Annales de l'I.H.P. Probabilités et statistiques

PY - 2010

PB - Gauthier-Villars

VL - 46

IS - 3

SP - 618

EP - 643

AB - The aim of this paper is to study the long-term behavior of a class of self-interacting diffusion processes on ℝd. These are solutions to SDEs with a drift term depending on the actual position of the process and its normalized occupation measure μt. These processes have so far been studied on compact spaces by Benaïm, Ledoux and Raimond, using stochastic approximation methods. We extend these methods to ℝd, assuming a confinement potential satisfying some conditions. These hypotheses on the confinement potential are required since in general the process can be transient, and is thus very difficult to analyze. Finally, we illustrate our study with an example on ℝ2.

LA - eng

KW - self-interaction diffusion; reinforced processes; stochastic approximation; self-interacting diffusion; reinforced process; stochastic differential equation

UR - http://eudml.org/doc/243319

ER -

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