A statistical framework for the description of stochastic resonance phenomena

Rung, Johan; Robinson, John W. C.
February 2000
AIP Conference Proceedings;2000, Vol. 502 Issue 1, p409
Academic Journal
We show how statistical distance measures known as &fgr;-divergences can provide a general framework for stochastic resonance (SR) type phenomena. The concept of ‘resonance’ is then generalized to mean local maximization (with respect to system and/or noise parameters) of &fgr;-divergences rather than signal-to-noise ratio (SNR) measures. This provides a general definition of SR which is applicable to virtually any kind of system/noise and it establishes a firm link to various bounds in information theory/statistics. Moreover, we show that SNR-based measures are upper bounded by a certain &fgr;-divergence and that ‘information conserving’ (invertible) systems like the classical double-well, preserve &fgr;-divergences. As a result, the resonance in the classical SR curve can be explained simply as the behavior of a non optimal detector in a case where the optimal detector has a monotonically decreasing performance. © 2000 American Institute of Physics.


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