  We analyze the strong noise limit of one-dimensional stochastic differential
equations (SDEs).
  Our initial motivation comes from continuous measurements of open quantum
systems. In this context, Bauer, Bernard and Tilloy pointed out an intriguing
behavior. As the noise grows larger, the solutions exhibit locally a
collapsing, that is to say, converge to pure jump processes very reminiscent of
a metastability phenomenon. But surprisingly the limiting jump process is
decorated by a spike process.
  We give a precise meaning to the convergence and completely prove these
statements for a large class of one-dimensional diffusions, thanks to a robust
strategy of proof.
