Transience, recurrence and speed of diffusions with a non-Markovian two-phase "use it or lose it" drift

2012/10/08 by Ross G. Pinsky, Pinsky, Ross G.
Mathematics · #60J60 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J60

paper · pdf · doi:10.48550/arxiv.1210.2443

arxiv created 2012/10/08 · arxiv updated 2012/10/10

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 +∞ 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 positive constant when the diffusion is sufficiently near its running maximum, and is equal to another positive constant otherwise.

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