The ODE method for some self-interacting diffusions on ℝd

Aline Kurtzmann

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

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

Abstract

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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.

How to cite

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Kurtzmann, 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 -

References

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