In this article, it is proved that for any probability law μ over R and a drift field b:R→R and killing field k:R→R+ which satisfy hypotheses stated in the article and a given terminal time t0, there exists a string m, an α∈(0,1], an initial condition x0∈R and a process X with...

In this article, it is proved that for any probability law μ over R with finite first moment and a given deterministic time t>0, there exists a gap diffusion with law μ at the prescribed time t.