# 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 (2014)

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

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topPinsky, 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 -

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