Haario, Heikki; Saksman, Eero Weak convergence of the simulated annealing process in general state space. (English) Zbl 0783.60069 Ann. Acad. Sci. Fenn., Ser. A I, Math. 17, No. 1, 39-50 (1992). The aim of this paper is to generalize the definition of the stochastic process corresponding to the original simulated annealing algorithm to the case of an arbitrary state space and study the weak convergence of the process. The results are expressed in terms of the generating distributions and the sequence of successive temperature parameters. At the same time we obtain estimates for the (Dobrushin) coefficient of ergodicity for an \(n\)th iterate of some important kinds of generating distributions. These estimates are also of independent interest. For most of the results the proofs are only sketched here. For full proofs see [authors, Adv. Appl. Probab. 23, No. 4, 866-893 (1991; Zbl 0744.60104)]. MSC: 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60B10 Convergence of probability measures Keywords:simulated annealing algorithm; weak convergence; coefficient of ergodicity Citations:Zbl 0744.60104 PDFBibTeX XMLCite \textit{H. Haario} and \textit{E. Saksman}, Ann. Acad. Sci. Fenn., Ser. A I, Math. 17, No. 1, 39--50 (1992; Zbl 0783.60069) Full Text: DOI