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.
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