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Hardcover ISBN:  9781470410490 
Product Code:  SURV/194 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470414733 
Product Code:  SURV/194.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470410490 
eBook ISBN:  9781470414733 
Product Code:  SURV/194.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 194; 2014; 189 ppMSC: Primary 60; Secondary 34; 37; 86
Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology.
This 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 optimizing 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.
ReadershipGraduate students and research mathematicians interested in large deviations and stochastic resonance.

Table of Contents

Chapters

Chapter 1. Heuristics of noise induced transitions

Chapter 2. Transitions for time homogeneous dynamical systems with small noise

Chapter 3. Semiclassical theory of stochastic resonance in dimension 1

Chapter 4. Large deviations and transitions between metastable states of dynamical systems with small noise and weak inhomogeneity

Appendix A. Supplementary tools

Appendix B. Laplace’s method


Additional Material

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Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology.
This 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 optimizing 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.
Graduate students and research mathematicians interested in large deviations and stochastic resonance.

Chapters

Chapter 1. Heuristics of noise induced transitions

Chapter 2. Transitions for time homogeneous dynamical systems with small noise

Chapter 3. Semiclassical theory of stochastic resonance in dimension 1

Chapter 4. Large deviations and transitions between metastable states of dynamical systems with small noise and weak inhomogeneity

Appendix A. Supplementary tools

Appendix B. Laplace’s method