Transience, recurrence and speed of diffusions with a non-markovian two-phase “use it or lose it” drift

Ross G. Pinsky

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 4, page 1198-1212
  • ISSN: 0246-0203

Abstract

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We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases – a transient to + ∞ mode which is activated when the diffusion is sufficiently near its running maximum, and a recurrent mode which is activated otherwise. We also consider the speed of a diffusion with a two-phase drift, where the drift is equal to a certain non-negative constant when the diffusion is sufficiently near its running maximum, and is equal to a certain positive constant otherwise.

How to cite

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Pinsky, Ross G.. "Transience, recurrence and speed of diffusions with a non-markovian two-phase “use it or lose it” drift." Annales de l'I.H.P. Probabilités et statistiques 50.4 (2014): 1198-1212. <http://eudml.org/doc/272037>.

@article{Pinsky2014,
abstract = {We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases – a transient to $+\infty $ mode which is activated when the diffusion is sufficiently near its running maximum, and a recurrent mode which is activated otherwise. We also consider the speed of a diffusion with a two-phase drift, where the drift is equal to a certain non-negative constant when the diffusion is sufficiently near its running maximum, and is equal to a certain positive constant otherwise.},
author = {Pinsky, Ross G.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {diffusion process; transience; recurrence; non-markovian drift; non-Markovian drift},
language = {eng},
number = {4},
pages = {1198-1212},
publisher = {Gauthier-Villars},
title = {Transience, recurrence and speed of diffusions with a non-markovian two-phase “use it or lose it” drift},
url = {http://eudml.org/doc/272037},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Pinsky, Ross G.
TI - Transience, recurrence and speed of diffusions with a non-markovian two-phase “use it or lose it” drift
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 4
SP - 1198
EP - 1212
AB - We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases – a transient to $+\infty $ mode which is activated when the diffusion is sufficiently near its running maximum, and a recurrent mode which is activated otherwise. We also consider the speed of a diffusion with a two-phase drift, where the drift is equal to a certain non-negative constant when the diffusion is sufficiently near its running maximum, and is equal to a certain positive constant otherwise.
LA - eng
KW - diffusion process; transience; recurrence; non-markovian drift; non-Markovian drift
UR - http://eudml.org/doc/272037
ER -

References

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  10. [10] R. G. Pinsky. Positive Harmonic Functions and Diffusion. Cambridge Studies in Advanced Mathematics 45. Cambridge Univ. Press, Cambridge, 1995. Zbl0858.31001MR1326606
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