Stochastic resonance : a mathematical approach in the small noise limit

著者

• Herrmann, Samuel
• Imkeller, Peter
• Pavlyukevich, Ilya
• Peithmann, Dierk

書誌事項

Stochastic resonance : a mathematical approach in the small noise limit

Samuel Herrmann ... [et al.]

（Mathematical surveys and monographs, v. 194）

American Mathematical Society, c2014

注記

Other authors: Peter Imkeller, Ilya Pavlyukevich, Dierk Peithmann

Includes bibliographical references (p. 183-187) and index

内容説明・目次

内容説明

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 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.

目次

Heuristics of noise induced transitions Transitions for time homogeneous dynamical systems with small noise Semiclassical theory of stochastic resonance in dimension 1 Large deviations and transitions between meta-stable states of dynamical systems with small noise and weak inhomogeneity Supplementary tools Laplace's method Bibliography Index

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB14368368
• ISBN:
  • 9781470410490
• LCCN: 2013034700
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xvi, 189 p.
• 大きさ: 27 cm
• 分類:
  • LCC : QA274.25
  • DC23 : 519.2/3
• 件名:
  • LCSH : Stochastic partial differential equations
  • LCSH : Diffusion processes
  • LCSH : Stability
  • FREE : Probability theory and stochastic processes -- Stochastic analysis -- Stochastic ordinary differential equations. msc
  • FREE : Probability theory and stochastic processes -- Markov processes -- Diffusion processes. msc
• 親書誌ID:
  • BA00134419