viii PREFACE

With this scope the book addresses researchers and graduate students in math-

ematics and the sciences interested in stochastic dynamics, in a quite broad sense,

and wishing to understand the conceptual background of stochastic resonance, on

the basis of large deviations theory for weakly periodic dynamical systems with

small noise. Chapter 1 explains our approach on a heuristic basis on the background

of paradigmatic examples from climate dynamics. It is accessible to a readership

without a particular mathematical training. Chapter 2 provides a self-contained

treatment of the classical Freidlin–Wentzell theory of diffusion exit from domains of

attraction of dynamical systems in the simpler additive noise setting starting from

a wavelet expansion of Brownian motion. It should be accessible to readers with

basic knowledge of stochastic processes. In Chapter 3 based on an approach from

the perspective of semi-classical analysis, i.e. spectral theory of infinitesimal gen-

erators of diffusion processes, the conceptual shortcomings of the classical physical

concepts of stochastic resonance are presented. In Chapter 4 the Freidlin–Wentzell

theory is extended to the non-trivial setting of weakly time-periodic dynamical sys-

tems with noise, and concepts of optimal tuning discussed which avoid the defects

of the classical notions. Both Chapters are accessible on the basis of the background

knowledge presented in Chapter 2.