Reflected Brownian motion with a drift that depends on its local time

Vi Le

Statistics & Probability Letters, 2019, vol. 154, issue C, -

Abstract: Consider a reflected Brownian motion with a drift that depends on its local time which solves the SDE Hs=Bs+∫0sf(Lr(Hr))dr+12Ls(0),where B is a standard Brownian motion and for s,t≥0, Ls(t) is the local time accumulated by H at level t up to time s. For x>0 define Sx=infs>0:Ls(0)>x and S=supx>0Sx.We give precise conditions on f, in order to decide whether the process Hs converges to zero almost surely as s tends to S.

Keywords: Reflected Brownian motion with drift; Local time; Branching processes with competition (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.06.022

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