摘要：Given any δ∈(0,∞), let (Xn)n=0∞ be the δ-once reinforced random walk on ladder Z×{0,1} with the following edge weight function at the (n+1)-th step:wn(e)=1+(δ−1)⋅I{N(e,n)>0}= 1ifN(e,n)=0,δifN(e,n)>0.Here N(e,n):=#{i1∕2 (Vervoort (2002) [8] and Sellke (2006) [7]), while the a.s. recurrence for negative reinforcement factor δ∈(0,1∕2] remained open. In this note, we give an affirmative answer to this question.
关键词：60K35; ladder; once reinforced random walk; recurrence
