000 02527cam a2200301 i 4500
001 135864
003 ISI Library, Kolkata
005 20150617114512.0
008 130828s2014 riua b 001 0 eng
020 _a9781470410490 (alk. paper)
040 _aISI Library
082 0 0 _a510MS
_223
_bAm512
100 1 _aHerrmann, Samuel.
245 1 0 _aStochastic resonance :
_ba mathematical approach in the small noise limit /
_cSamuel Herrmann...[et al.].
260 _aProvidence :
_bAmerican Mathematical Society,
_cc2014.
300 _axvi, 189 p. :
_billustrations ;
_c27 cm.
490 0 _aMathematical surveys and monographs ;
_vv 194.
504 _aIncludes bibliographical references and index.
505 0 _aPreface -- Introduction -- 1. Heuristics of Noise Induced Transitions -- 2. Transitions for time Homogeneous Dynamical Systems with Small Noise -- 3. Semiclassical Theory of Stochastic Resonance in Dimension 1 -- 4. Large Deviations and Transitions between Meta-Stable states of Dynamical Systems with Small Noise and Weak inhomogeneity -- Appendix A: Supplementary Tools -- Appendix B: Laplace's Method -- Bibliography -- Index
520 _aThis book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given by an exogenous periodicity of small frequency. Resonance, the optimal tuning between period length and noise amplitude, is explained by optimising the LDP's rate function. The authors show that not all physical measures of tuning quality are robust with respect to dimension reduction. They propose measures of tuning quality based on exponential transition rates explained by large deviations techniques and show that these measures are robust. The book sheds some light on the shortcomings and strengths of different concepts used in the theory and applications of stochastic resonance without attempting to give a comprehensive overview of the many facets of stochastic resonance in the various areas of sciences. It is intended for researchers and graduate students in mathematics and the sciences interested in stochastic dynamics who wish to understand the conceptual background of stochastic resonance.
650 0 _aStochastic partial differential equations.
650 0 _aDiffusion processes.
650 0 _aStability.
700 1 _aImkeller, Peter.
700 1 _aPavlyukevich, Ilya.
700 1 _aPeithmann, Dierk.
942 _2ddc
_cBK
999 _c418750
_d418750