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Author (up) Barrera, J.; Bertoncini, O.; Fernandez, R. pdf  doi
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  Title Abrupt Convergence and Escape Behavior for Birth and Death Chains Type
  Year 2009 Publication Journal Of Statistical Physics Abbreviated Journal J. Stat. Phys.  
  Volume 137 Issue 4 Pages 595-623  
  Keywords  
  Abstract We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discrete-time birth-and-death chains on a"currency sign with drift towards zero. In particular, this includes energy-driven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cut-off paths. Thus, for evolutions defined by one-dimensional energy wells with sufficiently steep walls, cut-off and escape behavior are related by time inversion.  
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  ISSN 0022-4715 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000272159500001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 78  
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