Alternative Approaches

  • Gerhard Winkler
Part of the Applications of Mathematics book series (SMAP, volume 27)


There are various approaches to stochastic relaxation methods. We started with the conceptually and technically simplest one adopting Dobrushin’s contraction technique on finite spaces. Replacing the contraction coefficients by principal eigenvalues gives better estimates for convergence. This technique is adopted in most of the cited papers. Relaxation may also be introduced in continuous space and continuous time and then sampling and annealing is part of the theory of continuous-time Markov and diffusion processes. It would take quite a bit of space and time to present these and other important concepts in closed form. Therefore, we just sketch some ideas in the air. Neither of the topics is treated in detail. The chapter is intended as an incitement for further reading and work and we give a sample of recent papers at the end.


Stochastic Differential Equation Large Eigenvalue Gibbs Sampler Small Eigenvalue Asymptotic Variance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Gerhard Winkler
    • 1
  1. 1.Mathematical InstituteLudwig-Maximilians UniversitätMünchenGermany

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