Abstract
We analyze strong noise limit of some stochastic differential equations. We
focus on the particular case of Belavkin equations, arising from quantum
measurements, where Bauer and Bernard pointed out an intriguing behavior.
As the noise grows larger, the solutions exhibits locally a collapsing, that
is to say converge to jump processes, very reminiscent of a metastability
phenomenon. But surprisingly the limiting jump process is decorated by a spike
process. We completely prove these statements for an archetypal one dimensional
diffusion.
The proof is robust and can easily be adapted to a large class of one
dimensional diffusions.
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